Correspondence, 1981-1990

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Correspondence, 1981-1990
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Mathematics -- History -- 20th century

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STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305
DEPARTMENT OF MATHEMATICS


1/5/1981
Dear- Professor Hsu

.Y-our letter arrived a few days ao o,' preceded b,: the elegant
card from your department. I Please covey my greetings to your col-
leagues.
Paul Erdos accepted your invitation to be an advisor. I'll see
him soon and ask. him to send you a paper. Can you take papers in
English, clearly handwritten but not typed? That may save a lot.
of trouble for some of- us. The Copenhagen ahnou'bement is very well
written.. I wish you can fulfill your objectives'. [Chinese care
too much for "honor" and "face", so it may hot be. so .:asy if you.
really want to have frank criticism. I have recently received several
papers from China which seow the authosX lack of education and self-
criticism. Dut these papers will be published in the major journals
in China.
I appreciate your -efforts to arrange a trip -for me. If I can
visit these places I told you (how about.Tsingtao also?) I am willing
to come. .'Tather any of.my family will con--: with ime depend on many
factors. In 1981 I may visit South America as well as Europe, so it
may not be easy to carry out all the plane. Since :I want to sppnd J
i-0t-Atime 9dring the autumn season in China. I may coke in the middle
of September and go south in October. If you could accomi -any me on
part .of the trip that -would be pleasant.
A few days ago I saw a copy of the translation of my elementary
book (the one you have). The book was published 16 months ago and
I remember you mentioned it in an earlier letter. 7'The copy. I. aw is
a reprint in Hupei. It is in4 surprising that nobody has ever
written me about the translation and sent me even one copy. [When
the Russians translated .my book, they first asked for permission and
later gave me a bank account in. Aoscow. They also,. ot" a lot of revi-.
sion from me.-] The translation is uety literal vil) and contains
Prany linguistic mistakes.- Also some of the misprints were copied, with-
out correction., I would like to write the person in charge of this
publication. Can you advise me the best way to deal.with this situa-
tion? to whom- should I-,write, etc. As you-said they are really poor
in manners and in reason.. This must be -corrected.
If your relative can find out the. place where the exhibition will
take place :I will send his stuff (not yet received). Oth-erwise I can
Sot because there are many such exhibitions and they are often not
known in this country. So It will-be impossible for me to help him.

Sincerely






COPY







HEINZ G'OTZE D-6900 HEIDELBERG 1
Dr. phil. Dr. med. h. c. Dr. med. h. c. Neuenheimer Landstr. 28-30
Mitinhaber des Springer-Verlages Telefon 06221/487225






Dr. Kai lai Chung
Department of Mathematics
Stanford University
Stanford, Califonnia 94305

USA 28th January 1981
Gtz/js



Dear Dr. Chung,

Thank you very much for your letter of January 21st.

Copyright matters in the People's Republic of China will not change
until they have set up an internal copyright system and then joined
an International Copyright Convention, as the Russians did in 1973.
Prior to this the situation in the Soviet Union was very similar to
the present one in the People's Republic of China.

Your critical comments on the Chinese translation of your "Elementary
Probability" were of great interest to me. The prices of the Chinese
books cannot be compared to our prices because they are not based on
a commercial calculation. They are set up according to other principles
- besides the fact that a book printed in the People's Republic of
China costs much less than a book publisehd in the West because of
the low salary level, whichlis less than 5% of the Western standard.

Thank you especially for your information about Hsu's work, which we
would definitely like to publish at Springer-Verlag. I will discuss
the question of royalty payments with Mr. Kaufmann-Btihler.

I will unfortunately not be in San Francisco this time, because I am
flying from Frankfurt to Beijing, and then via Shanghai to Tokyo.
From Tokyo I will take a direct flight to New York.

With repeat d thankr-ad best regards,
Yours since ley,








NATIONAL UNIVERSITY OF SINGAPORE


Telephone : 7756666 Kent Ridge,
Telegrams: UNIVSPORE Singapore 0511
Telex : UNISPO RS33943


Ref: U of M 175/51 (11)



4 February 1981



Professor Kai Lai Chung
Stanford University
Department of Mathematics
Stanford, California 94305


Dear Professor Chung

Thank ybu for your letter of 21 January 1981.

We are pleased to haver'your acceptance to act as
external examiner in Applied,Mathematics for the
Final and Honours Examinations for the degree of
Bachelor of Science. Your appointment will be for
the academic years 1981-2 and 1982-3.

We shall look forward to your assistance in the
examinations.

Yours sincerely




Wong Yoke Lum
Asst Registrar


WYL/111


cc Dean, Faculty of Science
Head, Department of.Mathematics
Bursar









AIR LETTER
AEROGRAMME
IF ANYTHING IS ENCLOSED
THIS LETTER WILL BE SENT
BY ORDINARY MAIL


C,
0-
-9 11I 81


St GAPOR
> Affix 0

ere z
`3 U
R 8


Professor Kai Lai Chung
... ............ ...........i5 3 0 ^ 1 .? .1^ .....................................................
Stanford University

Department of Mathematics

Stanford, ..California 94305





_-----------------_ ----------- ----- ---------- --------------------
-SECOND FOLD HERE -


PRINTED BY NANYANG ENVELOPES BOOKITC ';
SINGAPORE, 1. 98

SENDER'S NAME AND ADDRESS:-


_, .,. E __


f-AMBMff~xXQR REGISTRAR'S OFFICE
.""....NATIONALK UNIVERSITY OF SINGAPORE

KENT RIDGE
SINGAPORE 0511



FORM APPROVED BY THE POSTMASTER-GENERAL
SINGAPORE NO. AL-7


-.FIRST FOLD HERE -


N .







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305


DEPARTMENT OF MATHEMATICS


Dear lProf. Heyers


?/10/1981


I just heard on the intercontinental tele-
.phone that you have accepted our invitation to
the- berwclfach meeting in May/June. That is
good news. II. Bauer is coming too.
This made ma think that you may be able to
give me a ride from Tubingen to the place. If
so upon arrival in Frankfurt by plane I may pro-
ceed by train to Tubingen,(unless the time is
to late or I am too tired). As I have not been
there before I'd like to stay a couple of nights
to enjoy the church twoers! When my schedule is
fixed I'll write you again and ask you to make
a reservation. Getoor told me he .would visit
you too.
I must tell you that last year when Hans Fol-
liner showed me a copy of your book I was plea-
santly surprised. I have also been writing such
a book starting from Hunt process anid ending with
Brrwnian motion. It has just been finished. Of
course there is rmiuch overlapping but there is
also sufficient difference.

Sincerely*
























COPY







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305

DEPARTMENT OF MATHEMATICS

February 17, 1981
professor IHarald Cramer
Sjotullsbacken 15
11575 Stovkholm
Sweden

Dear Professor Cramer,

First of all, this is to send my wishes for your continued
good health and well-being in 1981.
"ith some hesitation I should like to request a favor from you,
on behalf of several friends, both American and Chirnese. You may
recall that some time ago I wrote to suggest the nomination of a
Chinese writer for the Nobel prize in Literature. ;-ou had very kind-
ly csnt his nape to someone in the Swedish Academy. This author has
recently spent three months (with his wife) in the U. S.t visited many
universities including Harvard, Princeton, Yale and Stanford. He gave
a number of lectures and there are now more interest. in his works.
...any volun'es of his novels and stories are being published in iHbng Kong
of which the first volume has already appeared. An' Ali,,rican professor
has cozipiled all his works. Some has been translated into English.
"Ile are now trying once more to find a proper channel to submit his name
'to the obel committee, together with various supporting docum-i:nts.
If: you think this can be done through the person you mentioned in ,our
last letter, we shall send these tcs directly y to him. Since we do
not know any other channel, we wonder whether you. would be kind enough
to forward this request to your colleague? 1We shall forward the mate-
rial if and only if ht wants to see it. Otherwise the efforts -will
be discontinued. I am sorry to trouble you with this matter which is
not perhaps of your personal interest. It is only b.cause we feel that
his nomination will do honor to both Sweden and China that we are mak-
ing this effort.
His name is Shen Cung-wen.

Lay I add that if for any reason you do not feel it is proper for
us to forward tie material, we shall not trouble your colleague with.
it. Unly if we get a positive answer from him shall we communicate
further with him.
With highest regards.

Yours sincerely,

.Kai Lai Chung






COPY






PROBABILITY
and
MATHEMATICAL STATISTICS Feb. 18, 1981
Kopernika 18
51- 617 Wroclaw, Poland
tel. 48-10-76



Professor K.L. Chung
Stanford University
Department of Mathematics
Stanford, California 94305
USA


Dear Professor Chung,

I thank very much for your nice letter. We are glad to hear
that you may visit Poland in June 1981. We have possibility
to cover your expenses within Poland, however we cannot pay
your traveling to Poland. We look forward to see you in Wro-
claw.




Sincerely yours


Urbanik


ZGUWr., W-w. z. 1007/217, A-4, 1000+5







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305


DEPARTMENT OF MATHEMATICS


~/>/' 9Sl


'vurali


I do not understand your last letter. You have just made two
changes on the two pages I sent you, both OK. What "version" are
you talking about? Since I will send this correction to Ann. Inst.
Fourier immediately, will you please answer the following questions:
(1) Did you or did you not send these pages to them? If not why?
[You received it from me long before the galley.j
(5) I have checked the article as printed against jour4 and my
corrections. It has incorporated most (maybe all) of your
corrections, but none of mine. The most obvious one is
the first disp]ey on p. '>. 168, where " Did you make these corrections that I found on the galley?
(3) You said that they asked for both copies. Did you send a
different one the second time? Is it possible that on this
copy you did not 'make those corrections? These are minor
alrights but what about the two pages I sent you which contained
ed a very serious mistake.
Since I must .take this up with theeditorial staff of the journal.
please answer these questions precisely. I will have to quote your
answers to them to find out what happened.


HTyp. (B) certainly was not proved
I intended to quote this so I am now
one page of further proof is needed.
been added to the article. T'hy should


in that article! Unfortunately
obliged to say that at least
Yet this addition could have
this happen?


Sincerely.


















COPY







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305
DEPARTMENT OF MATHEMATICS

biarch 3. 1981
Dear Doleans-Dsdes

I have to trouble you once mores about your and Meyer's old results.
Since I an; teaching a course on stochastic integrals using xiietivier's
German notes, and found several mistakes which puzzled me, and we need
to have the answers before the quarter is over, riay I. ask you to answer
soon?
On p. 92 of Senm de Prob. I (1967), the equality on line 11 is incomire-
hensible to re. By line ", X id the Potential part of the Riesz decomposi-
t6on of X. l- en there is no reason for the equality. If we use the Doob-
...eyer decompposion for the trivial discrete case, then ttne increasing proc-
cess A is predictable and the equality holds when X is replaced by A. If
this is correct, has the mistake been corrected in later versions of kieyer's
notes (with you)? Please give an exact reference. But it is incredible to
-;!e that ideyer could have made such a mistake, so please explain the equality.
Ilext, can you give a nontrivial example of a local martingale X such
that T reduces X and XImT= is not integrable? See the definition of local
martingale in Dellacherie-;Aieyer. II. There are trivial exa.:ples in which
T=G p.s.!
You need not bother with the rest of this letter unless you have seen
-.etivier's notes. On p. 1.43 he w-,anted to give a proof for the uniqueness
of the D-i. decomposition in the particular case there, but it is quite
wrong. I cannot correct it but if you can (ad hoc) let re known. Note
the increasing processes A and Al have continuous paths. The proof on p.
I.40 is also quite wrong since (7.1.5) is notoproved there. I have correct-
ed this but still do not know whether for a L' nartingale with continuous
paths, the integral
( ,tlMd

is definable? _etivier certainly did not show this. If you know the ans-
wer please explain. I have written Ki. about the mistakes.

Sincerely,













COPY







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305
DEPARTMENT OF MATHEMATICS


IMarch 19, 1981
Dear iviaisonneuve,

Thanks for yours of the .10th. I'd be glad to give a talk. i.y French
is getting worse (it was never good) so may I speak in English. You can
schedule it for the convenience of your department. I plan to stay at
least three nights at Grenoble, longer if Glover is available for excur-
sions to the surrounding areas. Are we driving to Grenoble from Oberwol-
fach? Then you know the schedule for the travel. If you want to stop at
certain places that is fine. Perhaps my talk should not be given on the
day of arrival as I need some time to prepare! A propos, please find me
a nice little French hotel in Grenoble, in due time. Looking at the may
I saw sone intriguing mountains between Grenoble and Turino (where I sup-
pose French and Italians fought many wars?). Can you find out if there
are good trains between these places? Thi' information will be useful upon
my exit from (renoble.
I hope you don't mind forwarding the inc osed letter to the proper
person. If it is a Madames please make apologies for me. She (or he).
suggested a feuille volante for the erraton. Do you agree with me that
this would appear too "sensational" which'\the mistake does not really
deserve. II wonder if anyone but moimeme Would discover such a mistake---
certainly not Rao or the referee.J So I arm asking .her to insert the erratum
in a more habituelle way. What do you th.4ik? I remember as editor I also
made a goof of your iMiS by sending in the inkrevised copy. This is probably
what happened. Ieveu was the editor and he did not suggest a single re-
vision although there were a few obvious misprints!
Finally a mthematical question. Can rou find an entrance law from
infinity such that under the law Brownian lotionn on the line with time
reversed will behave e-actly as Brownian motion. For exam-ple it is true
(not trivial?) that if-0 lim P(X(at) = 0 I X(t) = x } = 1 x, etc'. 0(=s- st, fel
t -> co
It would be nice to replace the limit above by an entrance law---of which
you are the renowned expert. Your pal Geto,or also thinks 1o.
See you in June.

Sincerely,










COPY







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305
DEPARTMENT OF MATHEMATICS

March 25. 1981
Dear Professor Hsu Li-tzes
I am waiting to see the first issue of your new journal. Please send
me a copy by airmail when It is published, and a few more (may be by ship
mail) to give to others later. Erdoe has promised to give me a MS on
random graphs. His ntae may be translated as ")C I] 4
He has no permanent address but you can list him as Hungarian Academy og
Sciences. Budapest* Hungary.
What is the meeting you are going to in Germany? Hamburg? where and
when exactly. It is too bad that we cannot meet there as I shall be in
Oberwolfach in June and then visit some other countries, returning here late
in June. Let me know about your conference.
My very old friend Chou hsiao-chien just wrote me that his college can
invite me to Soozhou and he can arrange a trip to Huangshan. I told him to
contact you but he said he did not get anything definite from your reply.
It is possible that he can make certain arrangements in Chiangsu-Anhwei-Che-
k ng. However the dates will be determined by me because there are certain
constraints. As I told you thqe best time to visit you is roughly September
15 on for a week or a little longerr (if we can go to other parts of Manchu-
ria as you :mentioned, or Tsingtao). Next Huangshan and Anhwei for a week
(which may include Wuhan), n9xt I:. -- Tp for two weeks. My wife will
probably come. I must say 'expect the Chinese to pay all our expenses in
China. I am willing to giv 14ctures as they want. Frankly speaking, I
think the Chinese Publisginrg Ao. of my book (books) should pay me a lot,
You can ask them to pay part q-f our expenses in China. Wu Rong told me that
the man in charge of the translation of my Elementary Probability is r
If you know him you can writ him on my behalf. Chou also told me that ase
author of these books I have/the right to object to the publication, namely
not to give my consent to sqch irresponsible action. I may do this.
I asked Erdos if he kn w'4aufman (the HIT HONORARY prof)& He said he
had not heard of him. 4^body here kbows about fuzzy sets. It is* to say
the best, a unproved prod ct./ Why should China follow such things when
she has so much to learn/ff lold theories"? It is clear that quite a few
Chinese in their desparatiOrn are trying to "get famous quick" by changing
into so-called new fields. 'In my opinion if they want to do so they will
have a better chance going/into computers etc. Do you agree?
Youx suggested that I/write a review of the translation of my book.
That is a very interesting suggestion if I have the time. Let me wait a
while. 7hen will the niekt Issues of your journal appear? I can send you
the second instalment oj my article, but it need not be in the second issue.
I intend to continue this an"' make it into a small book. I can have it pub-
lished in the U. S. later. i
Hsu Pao-lu's Col ected works will be published by Springer-Verlag,
There are some problems about some of the posthumpus papers. I may ask
you and Zhang to w;xe an article about Hsu's later years. Can you do it?

Sincerely,

COPY






STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305

DEPARTMENT OF MATHEMATICS


April '7? 1981
Dear Lars,
By the ti.me you get this you have had our MS.well over 3 months.
I don't mind it if the referee is really refereeing the paper as he
should. My experience with the Acta Math. is that not a single ob-
vious misprint or slip was pointed out, even though I should have
been grateful for. such. In the MS you have I have found at least two
such "trivial" slips which can (haW-been) corrected by changing a few
words. I am waiting to see if the referee detects these as a counter-
refereeing.
Farts of your last letter were illegible die to your handwriting
and rusty English spelling. I remember when we were young your English
was excellent and you were very proud of it. Apparently it has deterio
rated owing to disuse. I hope you are not offended by this observation.
Finally you need not worry about my visiting Sweden. The inter-city
flights in Europe are so expensive that I (we?) cannot afford it. I am
going to an Oberwolfach meeting and then spend a few more days in Gre-
noble and perhaps 'Paris. But..Sweden is jsu too far. !"egards to Eva.

Sincerely,
























COPY











April 96, 1981
Dear Hans,

I hope this letter takes less time. We had
just a Seminar on Stochastic Processes in Evan-
ston, conceived by me, organized by Cinlar and
attended by about a dozem speakers and many
listeners. It was a success and will be conti-
nued next year, and so on. The proceedings
will be published by Birkhauer (I made Peters
pay a lot for this). I hope this wil become
a U. S. counterpart of the Strasbourg-Paris one.
Perhaps you and Nagasawa can attend sometime.
This time there were three French: Jacods Azema
and Carmona. I found out the following:answers
to our invitations.

Azema (not sure but probably)
Carmona +
Pitman -
Rao
New additions (I wrote you already ,
Neil Falkner (Ohio State) +
Ed Parkins (UBC, Vancouver) +
I suggest we invite one or two more Britons:
A. T. Barlow, Statistical Laboratory,
Cambridge# England
L. C. G. Rogers, Dept of Pure Math.,
Swansea, Wales, England
I donXt know if they can come. Can you ask somte
East Europeans: koles and Romainians. Hungarians
if you think we still need more. But I don't
know the names.
Thanks for the hotel reservation. Tell Masso
sao that if he does not want to drive. I can
go with anyone by train* but I hope to go with
somebody as I don't know the way.







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305

DEPARTMENT OF MATHEMATICS


April 28, 1981
Dear Dr. Chen,

The inclosure was returned to me a few days .ago. What went wrong?
I ju st got the Final Notice of your meeting from you. It is very
thoughtful of you. There is a lot of probability there* particularly
BM1. Did I not tell you several years ago that it was no longer suffi-
cient to work on limit theorem for a sequence of random variables?
Only statisticians are still doing so (to their benefit certainly).
If you can teach some such couress (not seminars which I am sure will
be over the heads of 99 per cent of the audience), then Southeast Asia
will enter the modern era of probability. I wish you success. Are
you sure of your plans for next year?
Several Chinese probaUlists will attend your meetings Hou, Wang,
and maybe others. These people are sadly "stopped" by the Cultural
revolution. They really don't know enough outsied their very limited
areas. You can help them if you are not too oriental (hypocritical)
in dealings with them. Let me cite one or two examples. Hou "begged"
me to comment on his MS on Markov chains when I visited him. I spent
several hours on the very unreadable book and made several serious sug
gestions for revision. ActTally the whole book should be rewritten but
I realize that is impossible. Can you believe it that when the publish-
er sent the English translation for my opinion, not a single word was
corrected? ',ell one example is sufficient. Unfortunately due to the
feudal beaureaucratic evil habits in .China these people will find it l
hard really to learn from the west. "Face" is one problem and the sys-
tem of promote-and-prosper ( 4 1 ; I** ) is another. Being an Asian
yourself you may be able to understand such things and steer them into
the correct dierctions.'
If you want to publish an article in a C14iihe'6 iMath. journal I can
recom:,,end one which is being started ahd to which I have contributed
some lecture notes. But maybe Lee Kuan-yui won't allow you? Best re-
gardss



** They get promotions even if they publish trivial or 'P*ng
papers. Several papers sFent to me are totally wrong (in sad Ways)
and yet the authors are Bpromoted!: Maax






XdOJ





May 5, 1981
Dear Professor Metiviers
Your letter dated April 16 arrived on May 4, Thank you for the
invitation. iMy original plan did not include Paris and I am return-
ing to the states from Geneva. However, since Paris is the center of
the world I am glad to make a detour to see you and Neveu. The best
schedule is as follows: Arrive in Paris June 14- (Sunday), visit Ecole
Polytechnique on Monday, talk in NeveuXs seminar on Tuesday, return to
Grenoble or Geneva Wednesday June 17. I don't know where ralaiseau is
but should like to see la fameuse ddole. If you want me to t&1k there
I am also willing, but that is not necessary. Les Acoliers may not like
to hear me in English, and my French is bad. For NeveuXs seminar the
topic will be -The Feynman-Kac functional and Schrd'dinger's equation".
You have heard a part of this but I have new stuff.
Will you be able to pay my train expenses (first class) between
Grenoble and Paris? Please also make a reservation at a "nice little
hotel" in Paris for the nights of.June 14, 15 and 16, convenient for
our purposes. I o.pe you can get me a ,quiet, room for wall under 200
P. (with privatebath) if possible). Since I am leaving on UMay 28 there
is no time for you to write me judging from the last mail. You can
write Hans F6llmer in ETH to forward your message. I shall be in Ober-
wolfach lIay 31 to June 6, then with Maisonneuve in Grenoble. from June
8 to June 13, probably.
I hope we shall have some time to discuss, your Cours on stoachastic
integration. I am now doing expoentidl (super iaringaale and realize
that the condition that; for some X>0: E(exp(X(IMt.t.I vefify even when Mt = f f dB for Brownian motion B and a "nice" f.
S(,t]
If f is simple this is easy but if f is bounded, it is not clear. I am
sure that the situation is well-known but I have forgotten it. Another
point we found in class is2the following. Suppose Mt is a local martin-
gale and frrxaxx hxt supE(Mt) < o, it still does not follow that Mt is
a martingale. One must be very,:careful about such thingS.,
V:*ith best regards,

Sincerely,


P. S. I understand it is no longer necessary to go to some govern-
ment office on the Quai-to get any French money as in the old days.
Please arrange it in advance and remind Neveu of this. Last time I
talked in his seminar was 1976 I believe. SDUV-HIVMHaLv OINmwIxva

o. fo6 VIN'aOdIvO 'cr(1ONVIs
AiIS)MAINfl (IOdNViS







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305

DEPARTMENT OF MATHEMATICS



May 27, 1981
Dear Aizenman and Simon,

I received your preprint. Since I shall be away for a while this
is a quick response after merely glancing at it.

The key condition (1,11) mystified me. We did not need it and our
conditions are clearly stated in the paper. Do you mean it is a neces-
sary ingredient for the solution of the Dirichlet problem? Is so please
specify in what sense? You seem to study a larger class of V than we
did. What I want to make surethat in our context we did not miss any-
thing indispensable to the solution.

Judging from your comments on p. 6, you may have overlooked the factej
n the part where Hasminskii's and our papers intersect* his results are
particular cases of ours. His V is of one sign whereas ours is merely
bounded. For instance we showed the existence of a positive solution
to be equivalent to the finiteness of our u(Dsq*,.). We also have the
representation (1.12) you emphasized. Simon has the preprint.
My initiqls are wrong in [7], also please use "K. L." rather than
"K.".' This is a Chinese name not to be middled.
Finally please send a copy of uyur paper to Prof. K. M. Rao at the
Math Depts Univ. of Florida, Gainsvilles Fa. Thanks.


Sincerely,






STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305


DEPARTMENT OF MATHEMATICS


-June 22, 1981


Dear Lars,


I am shocked that our MS was lost after six months. Did you get
any referee's report on it? As I told you when submitting it there it
nobody in Scandinavia who can possibly 'read that paper (it requires both
nontrivial probability [not the Feller kind and knowledge of PDE). The
paper has already some sequels, one by me and >Li, the other by Aizenman
and Simon. You probably know Simon. lie thinks he knew probability but
of course he did not, but he is now learning. Since both ieir paper
and my other ohe will probably appear relatively soon I would have dto
ask you how long it will take for you (i) to referee tle MS (ii) to pub-
lish it before I can decide. I may send it somewhere else where it will
be quick.
Do you know any application of the Dirichlet firbt boundary value
problem for the Schrodinger equation.(with bounded*, ot negative qln
( + q)u = 0 )? If so you should really look at thd method and results
of our MS for your YEAR. Congratulations to Eva--- you inuboth be g ower-
ful now if not exactly rich. I just returned from Europe after visiting
Cberwolfach, Grenoble, Paris and Lausanne. I don't travel unless paid
for it., Even so the flight is too long for comfort, but we are going.
to China again this fall.

Sincerely,


COPY














June 22, 1981
Dear Aize-nman,
I received >1 copy of your joint MS with Barry. Since I came
back just from Europe it will be sometime before I can take a serious
look at it. It is certainly interesting.
Barry is probably jetting around so this is addressed to you and
L expect 4~ prompt answer.
(1) AKe your results for the Dirichlet problem extensions of ours?
I cannot budge from your conditions and assume that they overlap ours.
Also our results contain Knaiinskii's except possibl- in his case(q>0)
he may, not need that q is bounded (above). If you Know the precise
comparison of conditions and results please let me know.
(2) Not bdn'ag a math. physicist I cannot gauge the significance of
(1.11). Will y ou' please amplify a bit for our benefit?
(5) To se, there are true difficulties just consider the case where
m(D) = co (doieain has infinite volume). Have you got any results in
that case?
(4) You :isspelled my namein No. 6,> lso that paper has appeared
long since in Sm.i de P'rob. XTV. Please cite precisely. NM4so [7]
was abstract of a complete MS"which I gave to Barry several months ago.
It should appear in less than a year under the title "Feynman-Kac func-
tiinal and the Schrpdinger equation", by K.L. Chung and K. M. Rao., If
you want a preprint please let me know.
(5) ,Last byt not least my sincere congratutaltions for the advance
of mathematical physics into OPTIONAL TIMES (alias "first passage time")
Last time I kidded Barry a bit about its total absence in his excellent
book. True to6legend he had now learned its use with you. TMereversal
is the. NEXT step. Let me wish you full prberess and luck!

Sincerely$





(4a) 17ve you fond any applications of the Dirichlet problem an
physics? Wihen I first told Barry about our results .ore than a year
ago he Aaid there was (almtstO none. I hope he has learnede i I ce that
there are piLenty (and not just for negative q which is a trivial case).





Prof. Dr. H. Rost
Sprecher

UNIVERSITAT HEIDELBERG D-6900 HEIDELBERG 1, 31 .08 1981
SONDERFORSCHUNGSBEREICH 123 Im Neuenheimer Feld 293
Stochastische mathematische Modelle Telefon 562977









Prof. Kai Lai CHUNG
Stanford University
Mathem. Dept.

Stanford, CA 94305, USA








Dear Professor Chung,

I want to inform you that the faculty council of our department of
mathematics has agreed to offer you a guest professorship during
the summer of 1982 for a period of 1 2 month.

Usually, a guest professor teaches between 3 4 hours a week.
So, depending on how much you want to tell here, you may choose
the appropriate duration of this guest professorship. Independently
of this guest professorship which is offered by the Fakultat of
Mathematik, the Sonderforschungsbereich 123 can pay you from
different funds for some special seminars or research. The travel
expenses will be paid in any case. Maybe they are shared between
the Fakultat and the Sonderforschungsbereich 123. The usual
payment at the Sonderforschungsbereich 123 is DM 4.300,- a month;
what concerns the guest professorship of the university, it is in
the same order but it depends on salary (I don't know why).That
is the reason why I ask you to fill in the two copies of the
attached form and to send it back to me as soon as possible.

By the way, the payment of DM 4.300,-- is considered here not as
a salary but as a honorarium as far as tax and social security
are concerned.

I would be pleased if your intentions to visit our institute can
be realized; from our side we are rather interested in learning
your approach to problems of random environment.


With best regards,


. Dr. H. Rost








KUWAIT UNIVERSITY
DEPARTMENT OF MATHEMATICS

P.O. Box 5969 KUWAIT
c. 0.

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STANFORD UNIVERSITY
STANFORD, CALIFORNIA 4 /

DEPARTMENT OF MATHEMATICS
Professor Wang Shouren:

Your letter came when I was away. I waited until Liao .passed
his examination for the doctorate to give you the report you asked
for.
You recommended both Hsu and Liao to me in Beijing in 1979.. Your
judgment is excellent. They turn out to be both very good students
though they are very different in character and ability. At first
Liao may appear to be slower.. But I soon'found that he could learn
well and do research. 11e is thorough-going and reliable, and he has
shown considerable ability in solving problems and finding new results.
His thesis is on probabilistic potential theory, based on a paper by
me and Rao which I talked abott in Beijing. He has extended our re-
sults in several directions, completing and improving older results.
He has also studied certain questions about harmonic functions in a
general setting which is quite popular among French and German mathe-
maticians (not just probabilists). At his examinations people in p. I
d. e. showed interest and praised his presentation. He will go to the
University of Florida for a semester to advance his work with several
mathematicains there. He has already published a good paper in the
Sem. de Prob. and another joint one with me and Rao to appear soon.
His thesis will be published,:
Hsu Pei's young personality makes him more popular among his
colleagues here, and he is regarded as the best student in his class.
He is quick and communicates well, perhaps even a little glib (not a
serious fault in youth). He is strong in analysis as well as probabi-
lity which he studied in China. I gave him the topic of Neumann's
problem for Schrodinger's equation. This requires rather. different
techniques from those used by me and others for the Dirichlet problem.
With some help he was able to piece together a number of recent develop-
ments to produce a satisfactory work. Though he tends to stop too
soon, he is able to go farther when pressured. The result-is a thesis
much better than expected when he started. He has also done some work
in number theory. He will be in New York University .for the next- two
years. As he has recently married the daughter of an immigrant, it
is not clear when he will return to China.
More information about these two men may be obtained from Zhao
Zhongxin who returned to Beijing last month. Needless to says it is
very important that these well-trained and promising mathematicians
can continue to work and produce in China. My colleagues and I hope
to hear about their progress in the future.
With personal regards,


Sincerely*






COPY






STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305

DEPARTMENT OF MATHEMATICS




Ai /1# Feb. 20 1983
Dear David,

Thank you for your letter incl your letter to Hou. I am glad
to know that you are indeed going to China. I did not want to get
you invloved for fear that anything could upset an apple cart in China.
Now let me just breifly explain my remarks to Barlow.
'Hou never admitted that his "solution" of the "very difficult pro-
blem proposed by DK" was, ejected (let's not mince words) by the same
person. Instead he waS to argue whether the problem was indeed wvex
very difficult, as if I had belittled the problem itself. This is
clever communist (sic) polemique' What I.toldhim repeatedly, and ap-
parently also ,.y some otherd'7 is that his did not have a new solution,
but merely wrote out the 12-line Kingman'proof in long hand. It is
not a question of the difficulty of the problem, it is whether he has
solved it in any way which may be regarded as new {analytic or not).
It is clear that when he sent the proof to you and me, he thought
he had a new proof. This is rather foolish, but may be excused fran
his isolation and lack of peerf-discussion in Changsha. He published
his proof in a pompus way) and made much propaganda in the local papers.
That is Chinese politics. But after he had been told by you and me, he
still wanted to publish the same stuff in English. Theeditor made im
tone down his exaggerations on my advice' but I understand it has apear-
ed in the Chinese C. R. In a letter I wrote Hou a few week ago, I aked
him whether he accepts your evaluation if not mine? This is where you
camw in. He did not answer the question in another polemic reply, full
of Chinese nonsense. If Hou insists on bringing this caseup with yous
you should ask him the same question and get a Yes or No answer. If you
make it too diplomatically, I am afraid anything you say can be used to
save Hou's face and whitewash the facts.
Obviously Hou's case is not unique among Chinese scientists, as
the People's Daily shows in its columns. It is trivial in comparison
with what happened to 1Mathematics Research after the boss's daughter-
failed an exam. [You know them better than I do, but I heard the pro-
fessorreally wanted to pass her!] It is a sad comment on the society
though. Let us hope that your visit will do them some real good. Bon
Voyage. I'll most likely be in Canton from April 21 on for a few days.
Your letter contains no dates but if you happen to be there at about
the same times please contact me at Zhongsan University in Guangzhou
(Canton) through the Mathematics Department.

Cordially,




COPY





\-J. USERR
Universitat Fakultat fur
Bielefeld Mathematik


Universitat Bielefeld Postfach 8640 4800 Bielefeld


UniversitatsstraBe


Ruf (0521) *106-1
Durchwahl 106
Telex: 932362 unibi


Bielefeld, den 8'. 3. L '3

Az.:


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4429 ARISTA DRIVE, BAN DIEGO, CALIF'ORNIA 92103


10 July 1983

Dear Chung,old friends

thanks for your letter of
July 4 and for the Zoo passes. We are also members of the zoo
society, in fact we go to the zoo almost every day, we talk to
the guards and we are always up to date with the animals
gossip. We will keep the passes until August, for the event
that we have guests as it happens often during the summer;
after that, Ellen will give them to some of our neighbors who
can use them.

We are planning to go to Italy in September.
This will be my tenth return trip after I first came to the
States in 1946, and with all probability the last. This time I
will go first to Rome and look up some of my oldest friends
whom I have not seen for many years, including one of my
teachers who is still alive. I am 72 years old !

"Libiamo
Libiamo nei lieti calici..."

I remember very well the waltz from Traviata
and the meaning that it had for you and for our young friend.
What happened to her? She was an intelligent and delightful
creature, perhaps a little spoiled by college life.

Do you remember Gloria? That is quite another
type. She called me on the phone about one year ago from Los
Angeles. She was there with a guided tour trip and could not
come to San Diego.
She got a degree in German literature, then she
went to Germany and there she got married. She is now divorced
but still living in Germany. When she was at Cornell, at one
time she was living in the same building in which Marc Kac was,
and then he would address me as : "My dear neighbor in law "

So many memories; and still this is a small
package compared to what ties me to Italy. It has been a long
life and not altogether bad. The Cornell time has not been a
very happy one for me. This last is much better, in spite of
old age and of the little infermities that it entails. Ellen
has changed my life for the better.

Dear old friend: have best wishes and thanks
again.


CARLO RIPARBELLI







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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
CAMBRIDGE, MA. 02139



CHAIRMAN
PURE MATHEMATICS COMMITTEE
DEPARTMENT OF MATHEMATICS

August 4, 1983


Professor Kai Lai Chung
Department of Mathematics
Stanford University
Stanford, CA 94305

Dear Professor Chung:

I am writing on behalf of the Pure Mathematics Committee at MIT
to ask you for a letter assessing the work of Daniel Stroock, and his
suitability for a tenured appointment at MIT. We need a description of
his major contributions to mathematics, and a comparison of him with
others in his field who are at a comparable stage of their careers.
(Who are the best people, and how does he compare with them?) Informa-
tion on his teaching and on his general suitability as a colleague
would also be most helpful.

Our committee is currently investigating strong candidates in
several fields. Since there are very few openings in the department,
we may not be able to make an offer immediately even if, as we sus-
pect, his case is outstanding. Therefore we ask that you keep this
request confidential. We would like to have your letter by early Fall
so that we can get to work during the Fall semester.

We are fully aware of the time and effort writing such letters
takes, and we thank you in advance for your help.

Sincerely,



Victor Guillemin


VG:v







Universitat Fakultit fUr 4800 Bielefeld 1, den 22,8. 1 983
Bielefeld Mathematik UniversitltsstraBe 1
Ruf (0521) *106-1
Durchwahl 106- 5 0 12
Prof. Dr. W. Hansen Telex: 932362 unibi

Universitat Bielefeld Postfach 8640 4800 Bielefeld 1

Professor
K.L. Chung
Department of Mathematics
Building 380
Stanford University
Stanford, California 94305





Dear Chung,

so far my manuscript does not contain what I explained to you on the
blackboard since it is not clear to me which formulation would be
useful in the general case of a balayage space (where the process
is not necessarily a diffusion).

Obviously it is sufficient to know that there exists a base U of
open subsets U of X such that for every x E U E U there is a neigh-
borhood V cU of x and a real number c >O. satisfying

c-1 PCu(x, .) < P U(y,) < c Pu(x,-) (*)

for every y E V. Then every function hE + (X) which is harmonic
on a domain D in X (in the probabilistic sense) and finite at one
point x ED is continuous and real on D:

Indeed, we deduce immediately from (*) that the sets D n {h D n {h = o} are open subsets of D and therefore h < o on D.

Moreover, let xED, W open relatively compact, x EW, WcD,
w EW n C(X), w > 0, n E]N and
h = P (min(nw,h)) .
n Cw
Then h i's harmonic on W, continuous and real on W. Clearly the
sequence (h n) is increasing to P h = h. Let UEU, xEU, U cW
Cw
and choose V, c according to (*). Then for every y E V
0 < h(y)-h (y) = P (h-h )(y) < c P (h-h )(x) = c (h-h )(x).
n CU n CU n
Hence (h n) converges uniformly to h on V. Thus h is continuous
on V.







- 2 -


The condition (*) may not be very useful in a general situation,
but it is easily verified for the Marcel Riesz potentials where the
densities U of P (x,-) with respect to Lebesgue measure are
x Cu
well known if U is a ball: If U = B (a) then
2 2 a/2
a -r f x-a llY X -n l x-al pU(y) = (Ii y-al2-r2)a/
0 elsewhere

n
S-( I)n an
with a = 1 r(!)sin -- .






Sincerely yours



/V 771AAA^





AEROGRAMME

LUCHTPOSTBLAD


EXPEDITEUR (Nom et adresse) :
AFZENDER (Naam en adresy/ j'



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En cas d'insertion soit de feuillets 6crits, soit d'un
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NATIONAL UNIVERSITY OF SINGAPORE


Telephone : 7756666
Telegrams: UNIVSPORE
Telex UNISPO RS33943


Kent Ridge
Singapore 0511


U of M 175/51 (11)



1 November 1983



Professor K L Chung
The Department of Mathematics
Stanford University
Stanford, California 94305
USA



Dear Professor Chung

May I refer to my letter of 5 September 1983,
is enclosed for your easy reference.


a copy of which


I shall be grateful to know if you are able to accept the Senate's
invitation to act as external examiner in Applied Mathematics
as conveyed to you on 5 September 1983.



Yours sincerely




Wee Siew Choo (Miss)
for REGISTRAR

WSC/tlk



Eno.



cc Dean, Faculty of Science
Head, Department of Mathematics
Bursar












U of M 175/51 (11)

5 September 1983


Professor K L Chung
The Department of Mathematics
Stanford University
Stanford, California 94305
USA

Dear Professor Chung

It gives me great pleasure to extend to you once again, on behalf
of the University Senate, an invitation to act as external examiner
in Applied Mathematics in the academic years 1985-4 and 1984-5 in
respect of the following examinations:

(1) Final Examination for the degree of Bachelor of Science
(2) Honours Examination for the degree of Bachelor of Science
(5) Direct Honours (Intermediate) Examination for the degree
of Bachelor of Science

The examinations are normally held in February/March each year.

For the Final and Honours Examinations, the University proposes
to pay you a combined fee of S$750.00 each year. The fee for
assessing the Direct Honours Examination is dependent on the
number of candidates sitting the Examination. The minimum fee
payable is S$500.00 per annum (for a minimum of one candidate)
rising by S$100.00 for each additional candidate, subject to a
maximum fee of S$600.00 in toto. As we expect only one candidate
to sit the Direct Honours (Intermediate) Examination this year,
the fee payable to you for assessing this examination will be
S$500.00.

We hope that you will be able to visit the University once during
your term as external examiner. For your visit, we will book for
you a single return economy class air ticket California/Singapore by
the most direct route. If you are able to make use of a cheaper
means of travel, eg., an APEX fare, the University will, of course,
appreciate this. All arrangements concerning your travel and
accommodation in Singapore will be made for you by the University














- 2 -


on your behalf. While you are here in connection with the
examinations, the University will pay for your hotel accommodation
(no food but including government tax and normal service charge)
and a per diem allowance of S$75.00 for a period not exceeding
14 days.

For the year that you will not be visiting us, we shall send you
the answer scripts by air mail for assessment. The scripts should
be returned to us by surface mail. However, please send us the
mark list by air mail. The University will reimburse you any
incidental expenses in connection with the examinations.

The Head of our Department of Mathematics, Associate professor
Peng Tsu Ann, will discuss with you the academic details of the
examinations as well as the most appropriate time for your visit.

During your term as external examiner, the Vice-Chancellor would
appreciate receiving from you a confidential report on the teaching
and other aspects of our Department of Mathematics. In addition
to an assessment of the general level of academic standards, the
Vice-Chancellor would like to receive any recommendations you may
have on the Department's teaching methods, course contents, text-
books, library facilities and quality of the teaching staff.

I very much hope that you will be able to accept the Senate's
invitation and I look forward to hearing from you. If there are
any points which you may wish to raise with me, please do not
hesitate to let me know.

Yours sincerely



Wee Siew Choo (Miss)
for REGISTRAR

VSC/tlk

co- Dean, Faculty of Science
Head, Department of Mathematics
Bursar













San Diego 4 November 1983


Dear Chung:

Thanks for your letter of October 10
that I found here upon my return from Italy. We were there
almost two months: we left SD on September 4 and arrived back
on October 26, without incidents, although we had prepared
ourselves for the event that something might happen. We took
the health insurance "NEAR". Also, I opened an account on the
Bank of America which has branches in Italy and deposited there
$5000 for emergency for the event that we were robbed of our
traveler cheques, but nothing happened. When we travel, we keep
our traveler cheques in belts that we wear around our bellies,
under the shirt.

We heard lots of sad stories of ladies purses
stolen in the streets. Usually two men operate from a
motorcycle. One of them drives coming near the sidewalk, the
other grabs the purse. It is advisable for the ladies to keep
their purse under their arm and on the side of the wall, not on
the side of the street. By the way, this happened to Ellen
here in San Diego, in the parking lot in front of a market. The
force imposed on the purse strap was enough to make her fall.
The purse was lost with all her documents: driving licence,
credit cards etc. That was a major nuisance, to renew all the
papers.

In 1970, again here in San Diego, we were both
beaten and robbed. At that time I was an employee of GD-Pomona,
but I was at Convair San Diego on loan. We were staying in a
hotel in La Jolla and we were strolling in front of the hotel
near the ocean at 7 pm, after dinner. We were attacked by four
men who beated us badly and finally ran away with my wallet.
Such things happen everywhere in the world.

A dollar at its present rate, almost 1600 lire,
goes a long way. Eating in modest restaurants (trattorie) we
usually ate for 30000 to 40000 lire for the two of us.
Occasionally we went to more expensive places but without much
of an improvement or satisfaction.

I would recommend that you plan your trip well
ahead of time and make your reservations as soon as possible,
many months ahead of time. Places are likely to get
overcrowded, especially if meetings or big shows take place
there. We had to leave Rome a little ahead of time in order to
avoid a railway strike and were not able to find place to stay
longer until the strike would have been over.










Page 2


Our trip went very well, with much
satisfaction, but it was much too long for me. Beyond one
month, I do not enjoy my vacation any longer. Too many things
to be seen, too many people, old and dear friends, too many
emotions, too many discussions, too much food, too much wine
and too much staying up late at night.

We stopped to sleep -at New York both in going
and in coming back, in a small hotel near the airport, not too
comfortable, but it was a good idea. It is important for me non
to accumulate tiredness. So,-our stops were:

S.D. N.Y. Gallarate Venice Rome -
Ferrara Ravenna Bologna Genova Milano Zurich N.Y. -
S.D.

Gallarate is a small town near the Malpensa
airport (which is the airport of Milan) and we went there to
sleep and rest directly after the long flight from N.Y.

We have been in Venice many times and I always
return happily there. It is beautiful, as you know, and there
are no cars. The center is full packed with tourists but if you
walk away from it there is no crowd.

Rome is my home town and it is still beautiful
but the traf-fic is horrible. The trouble is that I know too
many people there and I have to run from a dinner to another
and stay up late at night. However there are a great many
beautiful things to be seen, and if you have a small background
of history, the ghosts come alive and they speak to you, of
greatness and of misery, of glory and of defeat.

We ran away from Rome and went to Ferrara, in
the North-East of Italy, on the line of Venice. Ferrara is
quiet and there are some beautiful things to be seen. We liked
it and it is good for a visit of two or three days, but I would
not care to go back there next year.

After Ferrara we went to Ravenna. There are
several splendid churches of the Bizantine period and style
(6th to 8th centuries). I used to like the city, but now it is
industrialized, they have discovered methane nearby, they have
made a center of export for vegetables. It is crowded.

After Ravenna we went to Bologna. It is a
beautiful city, reasonably quiet, now since about 20 years
under a communist administration which however does not give
you any trouble. Bologna used to be famous for its food, but












Page 3


now it disappointed me under that aspect.

Milan was another string of visits and dinners.
As you know, it is an industrial city, it does not offer much
to the visitor. It is a good place for working. The Cathedral
and some other churches are very beautiful. I went once more to
visit the Certosa di Pavia, an ancient monastery.

As a last stop we went to Zurich in order to
have a couple days rest without invitations and visits and also
to avoid possible delays due to strikes which plague Italy. We
flew back from Zurich to N.Y. with Swissair and we liked it
much better than TWA. Better food, more drinks, more leg space,
prettier hostesses.

I doubt very much if I will ever be able to go
back to Italy, primarily for financial reasons. If I were to
go, I would consider visiting Verona (very interesting),
perhaps Modena, and I would spend a few days on the Riviera,
for instance at Santa Margherita or Rapallo or Lerici. Those
are splendid places if you like the sea. Portofino is famous
but everything there costs three times as much as in other
places. You may always go there by boat from any of the other
stations. The Thyrrenian sea, on the West side, is more
colorful and rough. The Adriatic sea is more quiet and usually
mild.

I prefer Northern Italy to Southern because the
Northern provinces offer more comfort to the tourist. No doubt,
there are splendid places in the South. For instance Capri,
Ischia, Ravello, Amalfi. I have not been back in Sicily since
the war but the reports that I have from friends are favorable.
Anyhow, if I ever go there, I must necessarily hang around Rome
and Milan, but that is a personal boundary condition for me.

Dear Chung, It is always a great pleasure to hear
from you. In two weeks I shall be 73 years old but it is
difficult for me to realize that. My great fortune has name
Ellen. She takes care of me and of all my needs.

All my best wishes to you and your Family, and
a good hug from your old friend


---^






MATEMATICKO-FYZIKALNI FAKULTA UNIVERSITY KARLOVY
KATEDRA MATEMATICKE ANALYZY

186 00 PRAHA 8, Sokolovskd 83 Telefon 2316 034


C. V Praze dne

Professor
Kai Lai Chung
Department of Mathematics
Stanford University
Stanford, California 94305
U.S.A


Prague, October 12, 1985


Dear Professor Chung:


As you have been informed, we intend to organize a con-
ference on potential theory in Prague in the second half
of July 1987. We understand that a number of mathematicians
from abroad are interested in attending the conference.
The specialist programme will presumably include potential
theory in its wider associations. Accordingly, the confe-
rence will provide an opportunity for a meeting of specia-
lists working in the most varied fields of potential theory
and its applications. This is why it was found useful to
include in the programme one-hour survey lectures.


We should be very happy if you could deliver a lecture
reflecting the development and present state of the inter-
play of analytic and probabilistic potential theory. It -is
expected that the texts of the lectures will be published
in the conference proceedings.


If you are willing to accept our invitation, we will
contact our authorities requesting them to send you an
official letter of invitation. In this case the costs of
your stay during the conference will be covered. Unfortu-
nately we are not in a position to refund our guest's
travelling expenses and the expenses relating to the vi-
sits of accompanying persons.











We should very much appreciate if you kindly let us
your decision by 15 December 1985. If we do not hear
you within the delay given we shall have to assume
you do not accept our proposal.


We are looking forward to hearing from you.


Kindest regards.


Yours sincerely,


Josef Kr6l



Ivan Netuka


a oslav Lukes



jXri Vesely


Mailing address:


Jaroslav Luke6
MFF UK
Sokolovsk6 83
18600 Praha 8
Czechoslovakia


know
from
that












DRAZEN PANTIC
Lab 180/02
BORIS KIDRICH INSTITUTE
P.O.B. 522,BELGRADE
YUGOSLAVIA
20. T2.85



Dear Sir,
thanks for your paper on the Sturm-Liouville equation.I am working on my PhD.
thesys on the stochastic solutions of kinetic equations, so I have read your
books: "Introduction to Stochastic Integration" and "Lectures from Markov pro-
cesses to Brownian Motion ".In both books there is the statement that the gauge
u(f,D) is the unique solution of the Schrodinger equation, but without proof. As
I would like to study the proof in detail, I would highly appreciate if you send
me a reprint of your paper Feynman-Kac functional and the Schrodinger equati-
on".
My idea is to apply the techniques involved in solution of Schrodinger
equation to some other equations,like Dirac equation.(It seems that in that ca-
se I would have to integrate over the paths of Poisson process).This is motiva-
ted by the paper Relativistic Extension of the Analogy between Quantum Mecha-
nics and Brownian Motion by B.Gaveau,T.Jacobson.M.Kac.L.S.Schulman (Phys. Rev.
Lett. Vol.53.NoS.) which I intend to generalize in the multidimensional case.









Sincerely

Drazen Pantic

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bJL7


JOURNAL OF MATHEMATICAL PSYCHOLOGY 10, 241-264 (1973)




On a Class of Additive Learning Models:
Error-Correcting and Probability Matching'

EWART A. C. THOMAS

\'p .- Department of Psychology, Stanford University, Stanford, California 94305


A general model for learning signal detection in a Yes-No task is considered in which
(a) the decision criterion shifts upward and downward by equal steps, and (b) the
probability that the criterion shifts on a trial depends on the stimulus-response pair
on that trial. Conditions are given for this process to have a unique stationary distribu-
tion, and the behavior of the process, as the step-size decreases to zero, is studied.
The special model where criterion shifts may occur only on error trials can account for
5 the probability matching behavior and for the interaction between signal strength and
signal probability typically observed when the payoff matrix is symmetrical. Further,
when the shift probability is assumed to be an increasing function of the distance of
the sensory input from the criterion, the stationary mean criterion values are less
Extreme than the values that yield probability matching. It is shown that the model
provides a way of incorporating payoff matrix asymmetry. Finally, the standard error
in the maximum likelihood parameter estimates is calculated and a statistic is proposed
for discriminating the error-correcting model from the more general model.


I. INTRODUCTION

It is a common finding that subjects in detection, recognition and discrimination
tasks perform differently from the ideal observer, that hypothetical subject whose
decision-making behavior is optimal. One form of nonoptimal behavior which has
received some attention is that where subjects attempt to match their response proba-
bilities to certain event (stimulus) probabilities, rather than attempt to maximize their
payoffs. Probability matching, as this behavior is labeled, was proposed by Parks (1966)
as an adequate description of performance in a yes/no recognition memory task, the
data being analyzed within the framework of "signal detection theory" (Tanner and
Swets, 1954). Parks' rule is

p(S) = minimum[Kp(s), I], (1)

1 I have benefitted much from the very helpful comments of M. Frank Norman on earlier
drafts of this paper. I also wish to thank Donald D. Dorfman for allowing me to study a pre-
publication draft, and Mrs. Cecilia Bahlman for her technical assistance.
241
Copyright !) 1973 by Academic Press, Inc.
All rights of reproduction in any form reserved.


AJc(










December, 24, 1987


Professor K. L. Chung

Department of Mathematics

Stanford University

Stanford, California 94305, USA




Dear professor Chung:


I wish to express my gratitude for your appreciation of the

Russian translation of your book "An introduction to Stochastic

Integration".

Your plans concerning a second edition of your book are of

great interest for me. Though it is very rarely that a second

edition of a book appears almost immediately after the first one

in our country, I am eager to undertake necessary efforts to

attract the publishers' attention to the new version of your book.

Thus I should be very grateful if you send me two copies of the

second edition of your book which I need to get acquainted with

the changes and to be able to advertize the book.

It is necessary to mention that practically all copies of

the Russian translation of your book have already been sold.

I think that this circumstance will stimulate the publishers to

prepare the second Russian edition.


Yours sincerely,


V.M.Kruglov





Paris, le 24 Mai 1988


MOUIPE D'ANALYSE
United Asocide au C.N.R.S. N* 754
UNIVERSITY PARIS VI
4. PLACE JUSSIEU
75230 PARIS- CEDEX 05
TOUR 46 4* ITAGE
TEL. 336-25-25-POSTE 53-49
DF/CR


ENVOI DE :


Cher Coll6gue,

Le seminaire de theorie du potential de Paris desire ouvrir
sa publication A un plus grand nombre de math4maticiens ayant des int6rets
voisins mais varies.
II est natural, afin de garantirla quality scientifique des
articles, d'envisager la creation d'un comitg de r4daction.
Un autre role des redacteurs sera de proposer des orateurs,
lesquels front autant que possible l'objet d'une invitation.

Naturellement, comme nous le faisons dejA, nous accepterons
des textes ne correspondent a aucune conference. Nous rappelons que la
formule actuelle Lecture Notes in Mathematics Springer -, assure une
publication rapide et une large diffusion.

Nous avons donc pens6 A votre collaboration, et nous serions
tres honors que vous vouliez bien accepter d'etre l'un de nos redacteurs.
Nous sommes 6videmment ouverts a toute suggestion que vous jugeriez utile.

En attendant une rdponse favorable de votre part, nous vous
prions de croire A 1'expression de nos meilleurs sentiments.





Copie A Messieurs :


A. Ancona (Paris)
P. Benilan (Besangon)
N. Bouleau (Paris)
H. Brezis (Paris)
K.L. Chung- (Stanford)
C. Dellacherie (Rouen)
D. Feyel (Paris)
B. Fuglede (Copenhague)
M. Fukushima (Osaka)


N. BOULEAU



D. FEYEL


Y. Guivarc'h (Rennes)
W. Hansen (Bielefeld)
F. Hirsch (Paris
M. Ito (Nagoya)
A. de la Pradelle (Paris)
P.A. Meyer (Strasbourg)
G. Mokobodzki (Paris)
F. Murat (Paris)
I. Netuka (Prague)


F. HIRSCH



G. MOKOBODZKI











July 28, 1988 .


Dear Professor Chung:


In this letter I would like to express my sadness for the misunderstandings that have
arisen to disrupt our relationship. First of all, I would like to declare my continued great
esteem for you, both as a mathematician and as my mentor, and my sincere appreciation
for your invaluable advice and assistance during my Ph. D. work. I would also like to
apologize for any misunderstanding about what was required for completing my thesis and
I am glad to hear that this is now been resolved.

Furthermore, I want to emphasize my continued esteem for you, and my gratitude at
having had the chance to work with you for the past three years. You have continually
offered your support and assistance in many ways; for this, I remain deeply indebted to
you.



Sincerely yours,



Vassilis G) Papanicolaou







University Claude Bernard Lyon I


INSTITUTE DE MATHEMATIQUES ET D'INFORMATIQUE


Laboratoire d'Analyse Fonctionnelle et Probabilit6s

Lyon, le 26 octobre 1988


A.Goldman
a :

Monsieur le Professeur K.L.Chung
Department of Mathematics
Stanford University
Stanford, CA 94305, USA


Cher Professeur Chung,

Je vous dcris au sujet de vos travaux sur le movement
brownie en liaison avec le probleme de Neumann pour les equations
differentielles de type elliptique. Un de mes 6tudiants travaille
sur des questions voisines; de ce fait nous serions tres int4resses
a recevoir un tir4 a part de votre paper (6crit en collaboration avec
UH,, P i)l


Gauge theory for the Neumann problem
edit6 au Sdminaire de Processus Stochastiques de Birkhauser, ains:
que tout autre article ou "preprint" sur ce sujet. Serait-il 4gal
possible de recevoir un exemplaire de la these de Hsu Pei

Reflecting Brownian motion, Boundary local time and
the Neumann Problem.
J'ai adress6 un courier dans ce sens & Hsu Pei sans obtenir de r
mais peu-etre n'est-il plus au Courant Institute ?
En vous remerciant par advance, je vous prie de croirecher
Monsieuren l'assurance de mes sentiments les meilleurs.


L
ement


dponse,


A.Goldman


43, boulevard du 11 novembre 1918, 69622 VILLEURBANNE CEDEX Tdl. 78.89.81.24 poste 36.22 ou 78.89.20.71

FRANCE







Springer
Springer-Verlag
Berlin Heidelberg New York
London Paris Tokyo Hong Kong
Berlin,November 24, 1988
1020 sw


Professor
K.L. Chung
903 Lathrup Drive

Stanford, CA 94305
USA


440478


Spanish Edition: Elemantary Probability Theory with
Stochastic Processes, 1974
ISBN 90362-3



Dear Prof. Chung,

we are pleased to be able to inform you that we received
from the publisher Editorial Reverte, Barcelona, the
royalty statement showing the sales of the above mentioned
work in 1987.

12 copies were sold for which we received a royalty in
the amount of DM 27,08.

According to our agreement this amount is to be divided
equally between you and Springer-Verlag.

Thus, your share amounts to DM 13,54.

We have credited the above mentioned amount to your
account.

With best regards,
yours sincerely,
S ringer-Verlag GmbH & Co. KG




Hannelore chwarze
Royalty D apartment


Springer-Verlag GmbH & Co. KG
Heidelberger Platz 3
Postfach
D-1000 Berlin 33

Persdnlich haftende Gesellschafterin:
Springer Verwaltungs-GmbH, Sitz Berlin


Tel. Durchwahl : (030) 8207- Eingetragen im Handelsregister des
Tel. Vermittlung (0 30) 8207-0 Amtsgerichts Berlin-Charlottenburg
Telex :183 319 spbln d unter 91 HRA 175 und 93 HRB 7812
Telefax : (0 30) 8 2140 91 Sitz der Gesellschaften: Berlin
Telegramme : Springerbuch
Geschiftsffihrer:
Dr. Dres. h. c. Heinz G6tze, Dr. Konrad F. Springer, Dipl.-Kfm. Claus Michaletz,
Prof. Dr. Dietrich G6tze, Jolanda L. von Hagen, Bernhard Lewerich











November 30, 1988


Dear Professor Kai Lai Chung:

First of all I should like to inform you that, though with
a great delay, I managed to elucidate the question concerning
the royalty payment for the Russian edition of your book "Markov
Chains with Stationary Transition Probabilities". To justify
myself I must say that I received your letter with the correspond-
ing request only in october with a 10-months delay, the reasons
being unknown to me.
Your royalty payment, the amount kept in secret, is still
in the bank No. 7812, Moscow, Plyushchikha street, 42. More
details: you cannot convert it to dollars and thus you cannot
receive it in the USA. But if you happen to be in Moscow you can
receive it using the bank deposit book you mentioned in your
letter. Otherwise you should give power of attorney to somebody,
for example, to a citizen of the USA who is going to visit Moscow
or to a citizen of the USSR. You or your confidential person would
be able to receive it in roubles. This money cannot be converted
to dollars but can be spent in the USSR as you like. I should
remind you that the power of attorney must be certified in the
Soviet Consulate -or Embassy in the USA.
Concerning your second request I should like to let you know
that the royalty payment in dollars for the Russian edition of
your and Prof. Ruth Williams' book "An Introduction to Stochastic
Integration", as I was told, has already been sent through the
bank and you can receive it in your country.


Yours sincerely,



Professor Victor M. Kruglov

Zi ,//











THE UNIVERSITY OF MELBOURNE
Department of Statistics

Chairman: Professor Peter J. Brockwell






February 14, 1989


Professor Kai Lai Chung
903 Lathrop Drive
Stanford
California 94305
U.S.A.


Dear Kai Lai :

Many thanks for your letter of January 26th. We would be delighted to have you give a short
course on Brownian motion. I'm also sure we could put together a lively audience of 4th year
Honours students, graduate students and faculty.

We could certainly cover your travel and living expenses and arrange for accommodation in
Graduate House, which is right next to the campus.

The academic year here starts at the end of February and ends in late November. To get a
good-sized audience for your lectures PLUS hot weather, it would be best to start in early March
and go for about six weeks.

Intrigued to hear of Trudinger's antics. How have your eyes been since I saw you last? Look
forward to catching up with your news. We should try another wine-tasting expedition while you
are here. The wines are excellent. Let me know if next March-April sounds OK.

Best regards,


The University of Melbourne, Parkville, Victoria 3052. Telephone +613 344 6609 Telex AA35185 UNIMEL Cables UNIMELB






pj! ~ UNIVERSITY' DEGLI STUDIO DI FIRENZE FACOLTA' DI INGEGNERIA
ISTITUTO DI MATEMATICA APPLICATA
"GIOVANNI SANSONE"









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(i7?oS L 0yl)Ci


801944 Fe~-Vp~ .Mit, 3 cI 198A







UNIVERSITY OF LONDON

ROYAL HOLLOWAY AND BEDFORD
NEXW COLLEGE Egham Hill, Egham, Surrey TW20 OEX Tel Egham (0784) 34455



Department of Mathematics
Professors of Mathematics:
F.C. Piper, B.Sc., Ph.D., A.R.C.S., D.I.C., F.I.M.A.
J.W. Essam, B.Sc., Ph.D.
N.H. Bingham, M.A., Ph.D.
Professor K.-L. Chung, 3 July 1989
Mathematics Department,
Stanford University,
Stanford, CA 94305, USA


Dear Professor Chung,
I enclose a reprint of my recent survey paper
in Theory of Probability and Applications on Kolmogorov's work on
strong limit theorems. I would be glad of any comments.
I also have a question. One of the themes of my article (2,4)
is a comparison between the weak and strong laws. Many years ago I
saw a dramatic and amusing juxtaposition of two quotations from
'eminent authors', one saying (essentially) that the weak law is
feeble and should be discarded for the strong law as soon as possible,
the other that the strong law plays almost no role in mathematical
statistics. I made a real effort to locate this passage in time to
quote (or include) it in my piece on Kolmogorov, to no avail.
I have asked both our senior UK probabilists, Kendall and Reuter;
neither could recall the passage, but both immediately suggested
consulting you. I should be most grateful for a reference.
Perhaps I could also take this opportunity to enquire the
origin and meaning of a remark in your writings (alas, I am again
unable to locate the reference) contrasting the azure and the blue.
And as an enthusiast for fluctuation theory, whose liking for your
Course will be evident to you from the enclosed reprint, may I say
how much I enjoy that gem of exposition, your Chapter 8 on random walks.
I don't think our paths have crossed since the U of I meeting in
honour of Joe Doob in 1976. I trust that you are keeping well, and
enjoying your well-earned retirement.
Yours sincerely,






N. H. Bingham


Telex: 935504 Fax: 0784-37520










) STANFORD UNIVERSITY STANFORD, CALIFORNIA 94305-2140

DONALD E. KNUTH
Professor of The Art of
Computer Programming
Department of Computer Science
Telephone [415] 723-4367


May 4, 1990



Prof. Kai Lai Chung
Mathematics Department
Stanford University
Stanford, CA 94305-2125

Dear Kai Lai,
There's a famous story about a remark that once supposedly appeared in Math Reviews:
"This paper fills a much-needed gap in the literature."
But nobody in Ann Arbor at the present time has been able to locate the source of that remark.
Today I got a letter from a British mathematician who is pretty sure the remark originated with you. If
you indeed were the reviewer who made this great contribution to the literature, I think the fact should
be preserved.
Was it you? And if so, can you give any clues that would help me find it in print?
Thanks for any help you can give.

Cordially,



Donald E. Knuth
Professor
DEK/pw







STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305-12Z5

DEPARTMENT OF MATHEMATICS
(415) 725-6284
Dec. 20, 1990
Fitzsimmons:
I see that you have admitted defeat in your first historical
research. Since you are the only younger probabilist that I know
who reads the literature, may I ask you a question: have you ever
ascertained Wiener's oft-quoted proof of the path continuity of his
process? It was done by Fourier transform in his later books but
maybe he gave it earlier in his 1922/3 (hat here again your problem)
MIT journal. Is being young then* read them both but that was before
I learned the later approaches. In 1987 G. A. Hunt said to me that
Wiener did not really have its as such concepts as the ximxnixxil con-
tinuity of almost all paths were still unclear (as Hunt said). Would
you be able to find out whether Wiener proved the correct result in
so(m se e? Levy gave him the credit of this result and openly regret-
ted his missing it (read his autobiography).
In the first or second edition of Loeve's text in which he gave
a proof of this result (by the way it might have actually been in a
supplement by Loeve in Levy's book on PSeMB* first edition), he gave a
totally wrong proof. This I knew but t hope you can also check it.
I recall telling Loeve of his huge mistake: he proved essentially that
the path is continuous at all the rationals. A similar mistake was made
later by Dinges (know the name?) who even sent it to me. But at least
he was quickly disuaded by me.
I thought of asking Ron too about (1) Wiener, (2) Loeve, so please
show him the letter and GET SOME ANSWERS. These folks are long dead:
one can now speak one's mind without penalty.
Please answer soon, as your response might affect what I am writ-
ing in some historical remarks TO BE PUBLISHED. Thank you in advance
and HNY. By the ways you did not reply to an earlier request to deduce
the independence question (which we discussed) from all way from Tanaka
to whatever. Can it really be done?