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April 2, 1980 Hsu Pei, The summer quarter begins in the last part of June, but there may be no advanced courses given which will suit you. After you come you can find out what to do. If you want to live in a dormitory (this is the best way) you may have to register in the summer. In any case you will have ample time to prepare for your research. I do not know whether you have had courses in iarkov processes. You can start with my paper with Rao, A new setting for potential theory, which I lectured on (only about one third), and fill in the background from other books. Blumenthal and Getoor's book is more than sufficient. Meyer's T'rocessus de Markov is also very good. I understand that Della cherTe's book was studied in the seminars. If so here is a good exer cise for you to try. The result is known but maybe you can find a bet ter solution. Define the hitting time TA as usual, A a Borel set, and also TA = inf (t>O: X(t) E A). It is easy to show that for a Hunt process, the second is always greater than or equal to the first. Under Hypothesis (B), they are equal a. s. For a discussion of IHyp. (B) see Meyer's Frontiere de Martin (or ask Yen). In our paper we tried to prove (B) under our conditions, but we had to add a little more. Ahyway the exercise above is very interest ing because it is intuitively meaningful. It is surprising that the proof of equality under (B) is not so easy. One can learn a lot of things by trying to prove such a result. Here are some open problems in our paper which would be interesting. (1) Find a good condition under which the set Z is empty. One can even begin by assuming all paths continuous, but maybe the con ditions &n u should be strengthened also. (?) We proved that (B) is equivalent to: for each compact K: PK1 = UA where (AC K But maybe there is a simpler proof of this without first prov ing (B). Then the latter will follow. Someone 6ent me some stencilled notes on problems concerning our paper referred above. Unfortunately there were several errors. This kind of work is not easy and needs time for a deep understanding and to learn the techniques. It is a good way to think of such problems while studying the books. I hope there will be no further felay for your trip. Wh 1 ling waiting you may as well get started. Sincerely* 7?f 7/5/ 1 What made you want to edit a book of my work? Springer asked me some years ago and WSPC more recently. Of course I can do it myself. It sounds more "fun" (vulgar americanism. ) to have a former pupil as editor and commenfries by others. I may well do it but first a few A questions ese You can reply by mail or fax (650)8579532. No email. (1) Prepare a list of seleommwher due and by hom send it to me. I will subtract andladd. The final decision is mine. (2) Have you published any book yet? If not you will be shortchanged by the merchants but I can help you. If it is to be Yau's business "Inter national"'I suppose between Chinamen you can deal with him. (3) Other business B can be discussed later. If the published articles are to be just photo reproduced there will be "problems". WSPC did a good job in printing my book. I have not seen any book by Yau's Co. Tell them to send one for my inspection. Good Luck (you need it to deal with those sharpies). P. S. / call your interest in foreign language (I approve): can you re my recent article) in Italian? That must be in. I SELECT. read t Phone only when abs. nec. Yau's cohorts have been te@ering me with repeated unwelcome phone calls from Pekin etc.! Those Chinamen never learn. Q l ea FAX 6307895908 Hsu Pei: V 7/2/A This is in reply to your fax of 7/20. I would like to receive your list of selection before August 20, because we shall be away soon after till September x. It need not be complete. Your suggestion of a Chinese article is good: my very first math fubl. 1936/7 is available in copy and it would please me if you can translate it with my support. I will add a sad note myself, as my then good friend coauthor (son of famous Chinesefwhom you probably did not know) com mitted suicide sMKKxax before the article was written. I will also give you a reprint of my (so far unique) Italian article which will be included (without translation). There may be one or two short C. R. notes in French to be reproduced. This historical, reminiscent aspect of the collection is what interests me most. Beethoven said that he loved his 8th Symphony better than the publicly acclaimed 7th (or ?th). % Many ot r authors preferred their lesser works to popular ones. As Chin Sese scholar (not modern stupid Americani) you will understand this. Regarding commentaries, of course you must do one for my Excursion paper. I may do a couple for my dead coauthors  but I have not really thou ght about these possibilities yet  there is Tim However, can you set some "deadline" for the completion of your work, and I insist the publisher vl9 sets a deadline for the publication with heavy penalty fmr nonfullfilment (as in my recent contract with a big firm). These are the problems a novice author tends to overlooks but I will alert you when the time comes. Yau's firm would be OK if it (he) pays good royalties (which he did not to some authors, I heard). Your invitation is appreciated but let us simplify the matter by meeting for lunch in a nearby pace, Awerican st p. Today is Sat. next Thur. or Fri. is OK, just phone me at (650)857 M as early as you can and I will tell you when and where. See you t en. Hu Sen also wants the book, he says he knows you Pwell". k , 8474918906 Prof. Hsu, P. Math Northwestern 8/20/2001 Hsu Pei, I have looked over your list and checked with a few reprints in my file. Your selection is good especially in the later stage. In the earlier stage, long before your time, there are a few "popular" articles I shall add, and also a couple of my personal favorites9 Among the for mer category, have you ever heard of the RobbinsMonro method? Jack Wolfo itz was going around complaining about the unsolved problem of normal limit as hard as Riemann hypothesis. After I did it the statisticians immediate ly changed their tone saying that normality is not as important as their own (trivial) estimate .... That is the way of "statistiCs". There is a whole book of Cambridge Tract'(by an Indian) on it. Before I send you my revision, please let me know whether the articles are to be retyped on Latex or just photographed; take a look at my edition of P. L. Hsu's works. I was told by Springer Verlag that there are new compute er technology .... which I do not understand but maybe you do. If you prefer AMS/IP/ please tell me what books 44 (they) have produced and send me a good one now for inspection. If 'fc L er is the same as Yau's Hongkong business (which tried to get my book with Zhao), you better make sure that they pay good royalties. Of course we are not doing it for dirty money but there is no ,eason to let them cheat us out of their profit. X7 4 I am getting a reasonable one from a new edition of my Elementary Probabi lity. If need be, but after you have dealt with them, I can talk with them. A Regarding the total number of pages, the final decision is ours, not theirs. It 1/ooks there will be additional pages after my addition and subtraction. For instance, have you seen my "Mathematics and Applications"? I want it there as well as two Reminiscences of Levy and Do(e)blin. Many readers will read these rather than the other articles. My review of Doob's book may also be considered. We are going to N. Y. 8/23, and will be back 9/8. Mail will reach me at ( ) 30 White Oak Lane, Southampton, N. Y. 11968 / Tel. (631)2835911 [before noon N. Y. time] If possible send me a fax before or on 8/22. Regards, P. S. Do you want to include our unique joint artile (which you may com ment on!) iI v ^ w^^ October 1, 2001 Hsu Pei: The law of diminishing returns is operating so I stop. Just two more inclusions) one of which is up to you: our article on Neumann "C b 26 63 c/9Fzc] problem; the other "Crudely stationary counting processes" which is a A "refreshing". You are so efficient so maybe you can compile the revised list, with further suggestions + or as you see fit, send it to me before soMe So I wa=u? suggest commentators  please do also from your side. I will A A make copies the minor corrections oft the list and mail it to you in due time. Nothing important so please do not wait. As we have already discussed, let the socalled editor respond before we make any revision of our list. By the way, please feel free to make other suggestions at any time. I have made a copy of my Chiinese debut and found it rather difficult to read. If you agree it can simply be reproduced as a sort of museum piece perhaps with an English abstract? Of course if you wish to translate it that will be fine and I can help you with the obscurities there. Re the Italian article which you will receive soon, why not just print it as is  about time that 4 americans learn some foreign language! May I ask you to telephone Jing Qing at your area code (630)9609095? Ask her the status of the new end enlargedd edition of Green, Brown, and Probability that she is editing. If you don't feel like it just have one of your (Chinese) students do it ON MY BEHALF. OK? Thanks. IAll give you a copy when it appears. 6 u'w S= "Have a Good Day'." q I d p yiip 10/2/2001 Hsu Pei: Ig 4 I have no objection to includA that Lip paper. The Chinese title is / If you want a copy send 14 dollars and I'll get you one. I th ught Wu Rong gave you a free one. Continuous Parameter Markov Chains, Proc. ICM 1421 August 1958 Edinburgh, pp. 510517 (Invited address) My file of reprints is a mess. If you really want any of them, I can try to find it and send it to you. I will send a copy of my Chinese paper when I get to the office (rarely). I (we) have been to Marseilles many times, last time c. 1990 I gave a talk when there were at least three Chinese students. Do not let the take you to their "cafe" as the food (is inedible  my daughter said the same. What is the name of the director of institute there: Pr.. who dOes stochastic PDE  say hello to him. Bon voyage. If you really like history I can tell you many good stories, e. g. about Hadamard at the Boston ICM, 1950, He was in Pekin a year be fore I went to Tsinghua. Rick &.CA P t n et s r % = z .e Z  63 1 3. 630 789 39o8 Hsu Pei: Dec. 9, 2001 Your solution of the problem is mxx brilliant but you made a big misprint: "inequality")' The day before I got it Ruth found the EQUALITY in Riordan's book where messier proofs are given. I can now do it by a cute induction but yours is of course better. Is it new? This EQUATION was first given in 1795 [do you know the history of this year in Paris] at the Academie (with date when it was "lu") by two famous mathematicians whose names you will see in my article, cited in Todhunter's History where we probably saw it in China around 1935 (the year before the goddam japs invaded They still have not apologized when Kiang leming went there  he was too weak to insist on it but maybe he wanted to get jap yens ...?] A few years ago Bru (remember? O44btAa copy of the article but it was written in such a way (1795) that I could not decipher it. Now I read it and found that they stat ed their first (obviously basic) Lemma that is that EQUATION. They gave 5 special cases but not a complete proof, saying things like "there is no dif ficulty (to extend)... and so ,they Lwij ho(i the dettails). Now with your proof it is in fact "easy to see"J if fe formulateJ # as you did. But (Lale ttc arfe j ^rs) now I want to see how these two guys used the equation to prove the general proposition in our paper, namely: knowing that the Sun has risen n times in the first n+m aas, what is the probability that it will rise in r days among the next r+s days. We did that and the result is given  I have not yet checked to see if Mey gave the explicit result (as I said, the ar ticle is hard to decipher due to its style and "notation"). However maybe you can see how their Lemma would yield such a solution. 1955 was 66 years ago but I clearly remember that it took us a long time to do the calcula tion an iinally it was done by a kind of induction. I must now read that part (which I did not) to see ... So I must delay for a few days returning your list with suggestions. Ee my paper with Joe, of course I started it but he did something more: any Hunt process reversed becomes a leftcontinuous moderate Markov process. By the way "moderate' larkov" was first defined in my (cta .iath.) paper. So let us keep this and maybe ask Paul Andre Meyer to comment on it [I think he was the referee]. If necessary we shall sacrifice some other article. A\ /4P ? Dec. 18Q 2001 Hsu Pei: it g I will send you the two other pages of your list with suggestions. Your procedure of asking themguys is excellent but let me alert you to a cou le of things. I have suggested a few coauthors who may be too old to re spond, let them be. French guys are notoriously bad correspondents, even Neveu (my former "assistant" on a project) though he is very hospitable in Paris. Another person whose name I will withhold (guess) may respond in a selfserving semilying way i he sees that he has been shown up A nup (subtly) in my paper which WE ask him to comment. Some are so sloppy A ,e. g. Snell if you know him, very nice guy but sloppyYbut I am asking him to comment on my "Prob. and Doob"  he interviewed D. before I gave that talk in Urbana. Etc. etc. Let's see what, transpires. Paul'Andre is also a tricky type though not mechant. [Walsh used to complain that he favored French over American  John has a point]. OK my chores are done. I may later change my mind ... You did not mention in your latest fax whether you hak received the 173S 9en er 1, Chinese reprints. I worked hard on our proof of the Spnrise theorem, '1Ze? and am asw most pleased to discover that we had in fact proved that IDEN TITY in a different way than all the other proofs including the quickest one you found. I shall be glad to comment on it! r If you have any questions please let me know. 'A INPORTANT QUESTION: We have exchanged numerous fax(es?). P ease tell me if you have ever experienced any difficulty in sending yours to us? I have no problem at all sending mine to you (although some jerks have told me that they did not receive some of my fax  they might be lying.] So I "need to know" your experience/ (US government officialese) io4 \ 40O 7? 30..5 Jan. 16, 2004 Hsu Pei: . Re the stable tail, it should be proved without using ch. f. or Laplace or Suiordinator all that jazz. Feller tried hard (see Vol. 2) with out success. I proposed the problem to the rogs: Yor and Biane. Zero. Read Levy's original proof with those Poisson jumps la er the frogs made a big deal about. The result is stated in KolGne without proof. Of course if one uses the full force of the analysis of domain of attraction etc. maybe it will come out but nobody has ever seen it anywhere. FPtzsim mons and an Italian followed Levy's WAY (TAO) and maybe ... but that's not kosher as I said. Now if you want to test your own "force", try first the eaty symmetric case exp(Itla) and even the inversion formula (all in my Course) heuristically (1) to see what comes out. See Exercise 7 in Sec. 6.4 (?) where part of it is done: of course from the ch. f. near 0 (as you thought). Now get the rest of the tail if you can. I will tell Hou to double your "compensation" and shame those weaksisters frogs. Now a few (last) words about making copies. Who told you the big LIE that it can't be done WELL?? I made hundreds of pages from bound OLD vol unes years ago when you were a student. Everybody has done it. Have YOU tried yourself? As I said if "too busy" thepay a (Chinese) student to do it. Anyway, that is YOUR problem, eccoci. 'AtV V % \y/ 