Aleksandr Adolfevich Yushkevich, 1995

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Aleksandr Adolfevich Yushkevich, 1995
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March 25, 1995
Dear Prof. Yushkevich:
I received your letter with several reprints. I have not yet read
the latter but would like to reply first about other relevant matters.
I was told that your father was a historian of science and had assumed
that you knew some history. In Russia you all studied Mechanics if not
Electromagnetism, hence the two problems I asked you:
(1) Newton potential as integral of normal density in space
(2) Symmetry of Greenks function as electrical phenomenon;
[I am not sure of the spnd being this question], should belong to the
general knowledge of MATH. HISTORY. Young folks like Molchanov would hard-
ly know such things, nor would care. You must ask olds serious intellec-
tuals. Now I have tay or three more which you really should know:
(3) A good example where the strong MP was used in an early paper on
probability, Russian or otherwise* where it was not recognize as something
Strongg, namely not implied by the (weak) MP. Find say as many as you
can in the old journals. Q.
(4) It was known to me and Feller c. 1948 thatknown physicists like
Chandrasekhargs the astromer MIS-stated the weak MP s perhaps in his "fa-
mous" paper in "Selected papers in Noise and Stoch. proc." edited by Waxs
extremely popular in America. I even remember the big mistake in his state-
ment. Do you know ll it is? if not would you please read that paper and
try to find it? This is for a "double-checking". I will tell you his mis-
take if you do nat know and can't find it. Around 1949 a paper by a 4Mt
probabilist (maybe still alive) sent the Ann. of Math* Stat. a paper pro-
ving All sorts of wonderful results by the wrong definition. Feller and I
caught the mistake.
(5)An important step in SMP is to define the pre-T trible which is now
generally denoted by FT+ (see e. g. my Lectures 1982). But iou read Doob
's 1953 book in the chapter ofdcontinuous time martingales heimade a holy
mess of this field (=tribe). Hence it was not an obvious definition. Do
you know who and where it was first defined correctly? Give the reference.
T was called by the Russians (incl. you, I think) "independent of the fu-
ture". In the 1959 paper by Hksminskii he proved a lemma (later known as
his) using this concept, but I remember (though^net sure) that there was
a mistake due to misuse of the concept. If you have that paper will you
check it in Russianl[I read the English translation* often wrong---in many
places "continuous"="ndn-breaking" was translated as discontinuous!, also
in books.] As soon as I get your reply to this letter, I will continue
P&o "z Dftkk- v4k df J) J t j( CJIha






April 19, 1995
Dear Prof. Yushkewich:
Thank you for your letter of the 10th. Yesterday I sent you a few
reprints relevant to the strong Markov property and the tribe PFT "tribe"
is better than sigma-fields although it isPFrench originally], and an ar-
ticle in which the great formulas of Euler's were used to do something Kol-
mogorov did. The latter should please your father if he were alive. Pew
people now know these things. Regarding my question of integrating normal
density to get the Newton-Coulomb laws I am not surprised that Yaglom would
knowo. But your father should have. Now I am asking A. Well who knew a lot
CbWt certainly NOT all] about Euler's works (over 27 volumes]. It is possi
ble Poincare who knew both potential (balayage was his idea] and probabili-
ties [I have his Calcul] but still I am not sure that he had done that in-
tegral and SEE that it comes out Newton.
Now let me discuss FT. I am glad to see that you were the first to de-
fine it in such a simple ways but please give me a precise reference of its
"first occurrence" and if possible send me a copy of that occurrence. I
have checked again with Blumenthal's thesis which followed his MASTER Hunt'
s 1956 paper on Brownian motion [a great paper not fully appreciated, by
people like Eugene who mea~ly copied it and made facile extenAions]. That
silly idea of a function which agrees with some other up to the time T, etc.
on retrospect is "intuitive" but stupid. The fact not only Doob but also
Hunt missed the simple way )yours] means it is not so intuitive after all.
By the ways your remarks about Levy is of course correct but unnecessary:
he was knwon to reply on intuition but achieved most important results, even
if some contained serious mistakes. You mentioned one but in the 1951 paper
]motivated by my question] he also gave an correct proof of Austin's won-
derful theorem [my problem first solved by him] which I told him a nd he
acknowledged [in this respect Levy was a much nicer man than B. D., every-
Sonese]. There his mistake was not the SMP [which had been proved already
by me, but he used it anyway], but the fact that he mixed up a "last exit"
time with an optional time. Tts al l1J C3-opt-- J 'ue~
In the paper with Doob I sent you [also in my Lectures from MP to BM]
I gave another definition of FP which I am sure.you had not learned. Please
read it and comment. It begins with a totally general definition of FT
for any T. What is amazing (to me) is that when T is optional it yields
FT+ in the most natural way.
In your last letter you said you proved in your thesis (1953-1959) that
P' (t) exists if either qi or qj is finite. Austin proved these in 1953.






Analytically the simplest proofs are given in my book Boundary Theory for
MC [Princeton]. I knew you gave a counterg9imfgoA genral, but did you
prove any result about the first derivative when qi= C [Ornstein]
What prople do not know is: in the latter case the first derivative is of
no use at all. To my mind it is just a "hard" question without any conse-
quence, bn the other hand, in the case qi on MC. I have not seen the Kol. collection and now I can't read Russian any
more [I could very well in 1948and later]. If you can send me a translation
in German or French I would like to see it. I wanted to speak with Kol. in
Moscow but there was no time. I 'aw him again in Vancouver in 1974. He was
a good mans despite what Eugene complained about. Please tell me your opi-
nion. I read In Ley's 1948 book that it was A'incin who named Markoff for
the process.
It is impossible to discuss anything seriously with people whose sole
intention is egoistic. Neither Levy not Doob is like that. Doob is still
alive but he pretends not to remember things. Recently I discussed Borel's
original idea afout constructing Borel measure on the line'. goob had not
known that Borel's method had been carried out by transfinite induction
in 1949 by two portugese. Without Lebesgue's outer measure.
Assuming that you have Dynkin's book I would like to consult you on a
question. The problem of preserving the strong "eller property after kill-
ing (i. e. "subprocess" X =X for t and subsections and subsubsections with all sorts of remarks and supplements
[in the way the book is written: "niggardly" ---Rozanov also said so]. Ques-
tion is : after all these conditions (4.5.18 a (l)....4S*F) )'was there any
"tangible" result? Girsanov [now "famous"for his formula], Priouret-Correge
[Paris, now defunct], ... also wrote papers on the subject. Do you or any
of your Russian colleagues know such things? I will tell you the answer in
the next letter, but only after your reply.
'Please tell me the courses you are teaching, and who is there besides
you. I am retired and have plenty of time to do anything [this is USA], but
there are not many math'ns with whom I can discuss interesting topics. Here
is another little question: in your excellent expository book with Dynkin,
I think you asked whether there is an easy derivation of the Poisson on the
circle without harmonic function. Do you know now an elementary way? I know
one by Gegenbauer expansion but that is ,not elementary.
You were very kind to offer to re-ink your first letter for my poor
eyes. That is not necessary because if I tried hard I could decipher it.

t\ cj&






STANFORD UNIVERSITY
STANFORD, CALIFORNIA 94305-2125

DEPARTMENT OF MATHEMATICS
(415) 725-6284

June 13, 1995
iear Prof. Yushkevich:

It has been two months since we corresponded. You must excuse me
for forgetting some of the answers you gave me. It would take too much
time to find them and so I am asking you again some questions including
new ones.
(1) Was Serge Bernstein the actual professor of Kol. and Khintchine?
I tried to get his two or three volumes of rob ~ait'but Dynkin told
me that they were sold out n o-a o Was it Bernstein who FIRST rea-
lized that two-by-two independence did not imply "total independence"?
It sounds childish now but at that time I wonder? Did Pascal or Laplace
know the difference? An example was given by Bernstein, maybe in his book.
In 1906, ikn Einstein [contemporary of Serge B.] discuused his model for
Brignian motion he assumed only independence over two consecutive intervals
C [of a critical length tau], but obviously he thought that would imply also
the total inde ence over 3 or more such intervals. It is incredible how
careless these theoretical physicists could be. If Einstein could be so
careless about such a simple but basic hypothesis how could one believe his
more abstraAe gepmetrical hypothesis of sp'.e time?
(2) I asked you if you could find examples of the use of strong MP be-
fore it was correctly formulated, and you gave me only one example: the re-
flection lemma for BM. That is not satisfactory. There must have been
many other more important cases that physicists like F({rth [who ztrmaxxKatx
mx edited Einstein's papers] had employed. He derived the density of the
first passage time [which must be in his well-known book on diffusionqJ
but did he realize that decomposition formula! p (t) = jff(s)p (t-s)ds?
Of course these physicists always confuse things ight aa'Jby using diffe'
rental equations [Kol's or Fokker-Plamck] and make such simple but basic
arguments "a mess". They should really have concentrated on discrete, in
fact finite state space jai A. A. Markov did] where these notions become
more clear. Who cares for the real world' it is all just approximations
for them/tay (J ',
(3) I hope by this time you have 4-p able to find the very popular
book: "Noise and Stoch. Proc." by Nelson Wax which includes the article
yy Chandrasekhrt [and Doobs Ornstein, Uhlenbeck, ....]. If so could you
check whether the definition of process "without after-effect" is given
correctly, name nditioned on Xt=x, NOT on XtEA. Feller said Chand. got
it all wrong.
(4) It is well known that Ute Russian knowledge of western literature
in mathematics was very spotty. For some reason most Russians at that time
did not read the papers by the others, and of course vice versa. I am sur-
prised that you did not know the GOOD definition of F via P So far as
I know the Russians did not know thf work on predictable times and what
I called "mOderate MP". The latter was in Itaxx discovered by me when I
wanted to prove a version of SMP at the first infinity of a simple Markov
chaii. You studied this example too I think, after Doob's trivial construc-
tion, followed by some Jap. But very few probabilists know even to-day that
that is a critical case where the optional time is predictle and only the
MOderate form pf MP holds, as I proved it. a
'-U/f










(5) Kh. was born,1894, Kol. 1903.Markov's first paper on "chain "
wea published in Bull. Soc. physico-math. Kasans 2 ser. t. 15. No. 4 1907,
p. 135-156; Bull. Acad. Imp. Sc.. St.-Petersburg, 6 ser. t.l, 1907? p.
/
61-80. 9I took these from Hostinsky's Memorial des Sc. Math., Paris
1931. Frechet's book on chains refers to Hostinsky, being too lazy (as
French author) to list these papers in his own book [Borel collection
1938. I have both the latter books.]
I do not want to re-check Markov's paper which I read many years
ago, but I believe his problem [about mixture of balls in urns] had been
reproduced income Russian textbooks such as Gnekendo or Romanov's, if
not the later ones. II you happen to have this among your books and paper
can you send me a copy of the exact urn problem considered and solved by
M"arkov? The general method is expained in H.'s and F.,'s books cited above,
but I want the-original.
Next Kh. and Kol wvimall children when Markov published his 1907
paper. But you told me that they discussed that paper (in 1922? during
the Festival which you told me about, in which Markov was upset because
nobody listened to his speech on chains] and one did not want to name it
after M. the other did.- [In Levy's 1957 book he cietd Kh. as the origi-
nator of the name "Markov process".] Serge Bernstein also wrote papers on
"dependent" sums, but not necessarily Chains. 'So the queotion.I want to
ask you is: when was Markov's ideas about chains become accepted in his
own country? by people like B., KI, K2? You probably did.not know, but
I have found out that the same idea had already been introduced and many
results stated by Bachelier as early as 1912 in his GRAND Calcul ]which
I checked recently', He called it probabilitye connexe" a very good name
,not so different from "enchainee" He immediately considered continuous
time and Euclidean spaces but I do not know whether he had.proved any the-
orem' rigorously whcih generalized MarkOv's limit (ergodic) theorem that
we all know. In Frechet's 1937 book citetabove he mentioned Bachelier's
work on Speculation as one of the four or five different cases of chainsg.
Unfortunately he forgot to list Bachelier's ]l]s [21 [3] in his own book
and did not check with Hostinsky's list which did not have Bachelier at
all ]That could be politics or snobisna]
I/ F'-I A I;- Pw",k.








August 13, 1995
Dear Prof. Yushkevich:
I
I was astonished by what you said "You are wrong ... me (yax) told you

that Aarkov was upset because nobody ....". If it was not you who could i

possibly be? I am 100 per cent sure that I heard it in Gainaville while

talking to you about the Markov property. Was it not you that told me thai

there was a big fest Q(taii~ i iLenia and Markov gave a lecture ...???? It

is possible that you did not say that he was upset but I am sure somebody

eaid that nobody wanted to listen to .arkov because fireworks were going

off, eat~A xagNxwarx and people were havinra (typical Pussian ?) big carniv-

al. Lease try to recall if you did not aay that whio said it? I even ask-

ed when was that because Markov died (I think) in 1922, so that big celebra-

tion must be about some Rufsian/Soviet national event. What could it be?

T'ho was in Gainsville who could nave told such a etory except a Russian ---

besidcea yu was there any other Russian?
The question above has no mathematical or even historical interest, but
it has a great interest for me because my uiacory could not have been so bad.
It was you who told about the naming of the Markov process?
iy ilshrt book "Green, Browns And Probability" will boe Tablihed soon.
In one of the many footnotes I have stated thie information you gave D.e.
Tell your library to order a copy: it is cheap (iYorld Scientific Publishing
Co.). I th thinjr.ig of writing another one of the eamie kind, and mostly
about ciscrete prcvbewsN ouch as Markov ch~ain. In the infinite state case,
Roluiogor ov (3938) proved thfe ex istence of the limiit
p'". where d is the period :f i, as n-> o
but i'is proof uses prob4Sility and involves other states than i (his idea
is a "delayed renewal"). It wae Erdobs who first proved the result (publish-
eo with Peller and ollard) from t-;e rer:ewal equation of tte form
\): o V: ne r v n ere p aici f invol-.s only the st-te
i, nothing tel!e, k j -
Thus th~ei veI becr:&es .A purely aialytic one and in a certain sense better
than K.l'cL; ,hij.cr :reeos other ela-le. l~i.er there were other proofs which
I dc" not care for (coupling etc.) The 5-F-.- proof is given in .ty book* also
in T1]ler's Vol 1, lIt ed. But 1< later in the ,rd ed. [your library must
have that e ] he tried eo hard to ,(ke it rTore "lleleg"at" but succed4Led
cnly to make'it much rrore confs.'ing. '' o Yyu Know another proo. ? Hussian
textbooks a..e usually"poor" in this respect: either they copy, a known proof
or they o'.;it it (Shryiev :iiight hav omitted it) or give a special case (in
the finritc te te cs.ce, Markov''s l.7/ is cood but again involves other itateo
e). / Rsgardini SiPi Levy ib not a good example because his proofs are
always intuitive although often correct. I did t y~nkin's misuse of MP.
x ;i-4 Qt- c t f 4 A".i t
0^ le~pB1^Md;*9n







September 11, 1995


Dear Yushkevich [no "Prof." a la American]:
This time I reply at ohce because (1) I have too much time (2) you
are a good correspondent.
A third reason: of the 52 papers in Kol's collection, how many are in
prob. and related stuff, and how many are you familiar with? I have a major
proposal: you translate either all 52 or those you want to, and publish it
with my latest publisher:
World Scientific Publis ing Co. Sinbre, New Jersey,etc.
Tel. (800) 227-7 62.
I am almost sure that I can get it to publish it, provided tbat it has not
been translated into English before and published elsewhere. But I propose
that you add many notes, comments to the papers (those you know) such as
the subsequent work on those topics. I hope you will do it, and start atZ
once. If you agree, I can tell the publishers whose "BOSS" I know.
Only condition: you must do it very soon. Reason: I am very old.
As for my new book, you can tell your library to order a copy by tele-
phoning Dr. Ling at the number above. 5/r. ,rk4
Now a austake of yours: I did not say that Chandra made a mistake in _MP,
I said in MP, which is 10 times mo e serious. The mistake was to condition
on a set: TXEA instead on a value! Now please re-read his long physical
paper to see if that BIG MISTAKE was stilJ. there. It might have been cor-
rected. Anyway peqase read hi def. of the g [proc. without aftereffect]
very carefully to s~e T It s s correct Please etn tell me. Many others
ma Ti~ e i'stT ake, incl. a known Israeli, see my new book where the name is
given.
You compared the naming of the MP with that of the subway. It is not
clear what the MOTIVE of Kh./Kol. was. Please tell me again.
I hope you will translate the Kol papers! That will be a very good
project. If you wants and only if* I am willing to cooperate on this.
That would also kill some time for me. You will also earn a little money.
It is what the Americans call "win-win" thing.

(a- -A/ / ^7- V


I1 I '- II


'/


t Cu 7 d& & 2' Jl




iCu/2zt V (.^ ^^ f


4







kltA^ October 12, 1995
Dear Alex**:
I sent you a letter yesterday, but today while I was throwing out all
sorts of junk I found the copy of Markov's biography you sent me long ago
w1ich somehow I had not read (don't forget I am very old). Now that I look-
ed at it [you should understand what that means, it is not the same as "read"
and I am sure there is a Russian equivalent)* I must pick a bone with you.
First I must say that I am not like Eugenne and generally did not take cre-
dit for everything and very rarely engaged in so-called "priority" disputes
such as you had hinted about other math results (for yourself, for example).
No. I, on p. 129, you gave 'ynkin, Ito", but not Hunt r-Kakat~anw Your
article was written long after Hunt's 3 fundamental papers (19 ?) which
was translated in Russiant Hunt did much more fundamental work on continue
-ous time MP than Eugene ever did or could claim ---- you may ask Doob if
you want another authority. For example, the measurability of general
tionnal times using capacity was hunt's idea, Eugene merely copied him. Let
me quote Hunt in his own words: "What Dunkin wrote in one hook (the founda-
tions tittl-e book about 100 pages) I did in one section." Check it yourself.
Nearly all the basic ideas such as right continuity* quasi left continuity,
... for a general MP was Hunt's [not even Doob's altho the latter proved some
important results about right continuity [transfinite.induction]. Doob is
an hnest man and openly admitted that he was too stupidr to contract a
general process [known now as Hunt p.] from his results. Read the begniing
of Hunt's first memoir for the history. Ito did fundamental work on his f,
but he DID NOT do much about MP. You were wrong there too.( Y.* (t )
Next, on p. 130, for books on M. chains, youcited Kemeny (dead) and
Snell 1960. My book on M. chains came out in 1960 too* did you not see it?
I even gave Eugene a copy. It seems that you deliberately omitted it, why?
The book was translated by the people in Siberia (I will tell you a few sto
ries about Saka... laterif you want) and by the time you wrote the article
you should have seen it. I believe that omission is Soviet-political. You
can now tell me the PRAVDA. Quite frankly I do not mind such things, but
am curious why you did it. The reference to Loeve's 1955 book is, allow me
to say its funny. That was before a theory of MP EXISTED (Hunt). Again I
think that reference was inspired by Soviet-political considerations.
Do you know much about classical (and modern) Russian novels? With
kind regards,
X As I told you, the normal US way is to use the family name between pro-
fessionals who are not intimate" freinds, but it is common US custom when one
writes a critical or "unpleasant" letter one tkhSuses the intimate form delibe-







rately as euphemism. Here I am doing this as a joke. When I say Eugene,
it is for the same effect.













As an excellent exercise, please find the big mistake in the inclosed
page, and please return it with your answer.
^a ~-f^ .'*.






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Ae is togile srtne@i8eaWta Is chiackjbdbhdaa deatbqok
ln i n Pprob., I found that he had omitted the proofs of many important theorems.
How can such a book be good?
(4) I hope you will get the permission to translate. I know very well Kol's
German papers and Italian paper. Did you know that in his first (c.1929)
Paper in Math. Ann. he made a BIG mistake about an inequality which he tnen
corrected in a s tricky way in a second paper, both about law of LNS.
I put his inequality in my Course. These are great papers. But his more
famous paper (c. 1950) about MP's with the differential equations, later im-
proved by Feller, is not a great paper. It is famous only because people
like Chandra, Uhlenbeck, .... could only understand such analytic things.,
His It aian paper is also greats little known. (1,, )iff o
(5) The only Russians I knew a little are: Rozanov, s one
of the Yagloms (whom I took to visit Polya). I invited Rozanov to the Stat.
Dept one summer. He told mrthat his wife was Jewish but many Americans at-
tacked him as antisemite because his mother was a VIP. True? Rozanov told
me that Dynkin was caught doing a criminal act at the math inst. Is that
true? It is not important but one needs the PRAVDA. Rozanov was at a meet-
ing in Italy with me, just at the time of the collapse of the soviet commu-
nism, he had the chair of Kol's. Maybe he can give you the permission??
I was in China when Dobrushim was: he is a bit naive but I think an honest
guy. Dynkin obviously did not like Kol. although I heard that Kol. helped him
a lot --- I think Dynkin wanted Kol. to help him even more. ,'hat is the tru-
th? Could Stalin have a person like Kol executed publicly?? I donkt know.
I dislike some of the older Russian math'ns who visited ai Stanford such as
...*they were so "official". Linnik was all right but also naive. When Pro_
iorov was in Berkeley he asked for a prostitute (Neveu told me).
(6) It is your turn to tell some good stories. ~Si t. lAr en Stir i( I)


\\4V t

\.n"^Q







Here is an unsolved problem: let G(xy) be the Green's function for
a bounded domainDin the plane: defined for all (xy) [not just in D)
hx Prove at least that for each fixed x in D, as a function of y in R
it is upper semi-continuous.
If one can do this special cases then generalize to Greenian domains.
Only in the case of the 3-space, and only then for a bounded D, the result
is known. Of course if D is regular it becomes trivial.
I have asked three good young prob'sts: none can solve it. If you can't
please send it to a strong Russian in Russia [such as Linnik].




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