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DEPARTMENT OF MATHEMATICS
NATIONAL UNIVERSITY OF SINGAPORE BUKIT TIMAH ROAD, SINGAPORE 1025. REPUBLIC OF SINGAPORE TEL: 2560451 EXT. 344 20 November 1980 Professor Kai Lai Chung Department of Mathematics Stanford University Stanford, California 94505 U.S.A. Dear Professor Chung, Thank you for your letter of 5 November 1980. We appreciate your difficulty in making a trip here in 1981. However I am glad that I have telephoned you and we are very happy that you will be able to accept our invitation to be the External Examiner in Applied Mathematics for the academic years 1981 82 and 198283 (approximately 1 July 198150 June 1983). My Head will notify the University Administration of your acceptance. The Administration will later write to you. As regards your visit to our Department any period (of two weeks) between 1 July 1981 and 30 June 1983 (approximately) will be acceptable to us. I understand from the Administration that you are free to choose your itinerary provided the University is responsible for a part of your travel expenses equivalent to an economy class return fare of a direct route from Stanford to Singapore. Generally all travel arrangements are to be made through the University's travel agent. However, if you want to combine your trip to Singapore with other visits and your itinerary is complicated, it is possible that you make your own travel arrangements. The University will reimburse you later its share of the travel expenses. We would very much appreciate it if you could let us know at least three months in advance the period of your visit and whether you would like to make your own travel arrangements. In one of your previous letters you have indicated your preference to visit us during the term time. I enclose a copy of the calendar for the academic year 1981 82 for your reference. The calendar for 198283 will be about the same. We look forward to seeing you in Singapore. With best regards. Yours sincerely Louis H. Y. Chen cc Professor H. H. Teh Head Department of Mathematics ~2K,4~H.~K Ck&t~ NATIONAL UNIVERSITY OF SINGAPORE Ref: 57 Kent Ridge Singapore 0511 1 October 1980 Heads of Departments Principals/Masters of Halls of Residence National University of Singapore Dates of Terms 19812 and University Holidays 1981 SThe ViceChancellor has declared the following dates of terms for the academic year 19812: Term I : 6 July 1981 24 October 1981 (16 weeks) (Recess: 30 August 1981 6 September 1981) Vacation : 25 October 1981 22 November 1981 (4 weeks) Term II : 23 November 1981 13 March 1982 (16 weeks) (Recess: 25 December 1981 1 January 1982) *The following days will 1981: New Year's Day Chinese New Year Good Friday SLabour Day Vesak Day Hari Raya Puasa National Day Hari Raya Haji Deepavali Christmas be observed as University holidays during. 0oo0 0*@0 .O.. ...e +Thursday,.1 January' +Thursday, 5 February Friday, 6 February Friday, 17.April Friday, 1 May Monday., 18 May. +Saturday, 1 August *+Sunday, 9 August +Thursday, 8 October Monday, 26 October +Friday, 25 December Lu Sinclair (Mrs) Registrar WYL/elct * Where a holiday falls on Sunday, the next day following shall be a University holiday +. Holiday falling in term time cc Deans of Faculties Directors of Schools Students' Union 862/80 NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics Telephone : 7756666 Telegrams: UNIVSPORE Telex : UNISPO RS33943 4 July 1983 Professor Kai Lai Chung Department of Mathematics Stanford University Stanford, California 94305 U. S. A. Dear Kai Lai, I was very pleased to hear from you again. viewing Lou for us. From your letter, he seemed interview. I do agree with you that we must get people for our Department. Thank you for to have passed the right kind I don't see how you could stand 42 hours of travelling by train (from Wuhan to Kunming). Annabelle and I took a day train from Nice to Paris and then a night train from Paris to Lucerne. The total number of hours of travelling was less than 20 and we thoughtit was the limit for us. I don't recall that you have written me about a Cheng who wanted to study with me. I am curious as to why he wants to come to Singapore instead of better places in the U.S. or France. If he is a Chinese from China, I am afraid it will be difficult for him to be admitted by our University. I have read your article about Hou. I am sorry that he has done the things you have described. I hope that young Chinese mathematicians will learn from your article. I have met the two Chinese students of Meyer. One of them is Zheng Weian ( p ) who is in his earlier thirties and whom I had the chance to get to know better than the other. He appeared to be humble, discrete and honest. My acquaintance with him has led me to the belief that there are many young Chinese mathematicians who possess professional ethic and intellectual honesty. I do not have a new version of my inequality. But I do have a few more special cases including one on the simplex a counterpart of Wirtinger's inequality on Sn. I have also generalized the inequalities for the normal distribution and the Poisson distribution to those ...2/ Kent Ridge Singapore 0511 inter your of  2  involving higher order derivatives and differences respectively. This direction of generalization has led me to consider stochastic multiple integrals involving several independent processes. (Ito's Wiener multiple integrals which relate to the Hermite polynomials involve only one process.) I have obtained some results concerning such multiple integrals by an approach which I discovered myself. I do not know whether the results and the approach are really new, since my interest in stochastic analysis is very recent and I am learning the subject while doing research in it. I will write you later about the results and the apporach. I feel very honored that you have asked me to serve on the board of referees for.the PaoLu Hsu Prize. The reason I hesitated to agree to serve on the board when you first asked me in Singapore was that I felt my achievement was too little to deserve such an honor. However I have given this matter some thought and have convinced myself that one can contribute to mathematics not only by research but also by providing encouragement and opportunities for younger mathematicians. In the light of this, I have decided to agree to serve on the board of referees. I would like to thank you for asking me. I presume that I will be hearing from you at a later date concerning details of the Prize and my responsibility. You should have by now received my letter requesting you to continue as our external examiner. We hope that you will kindly agree to do so. With best regards. Yours sincerely, Louis H. Y. Chen P.S. Peng Tsu Ann has received your letter which you wrote from China. He has written you a note a few days ago. NATIONAL UNIVERSITY OF SINGAPORE DEPARTMENT OF MATHEMATICS Telephone: 7756666 Lower Kent Ridge Roed Telegram : UNIVSPORE Singapore 0511 Telex : UNISPO RS33943 Republic of Singapore 10 March 1988 Professor Kai Lai Chung Department of Mathematics Stanford University Stanford, California 94305 USA Dear Kai Lai I am sorry for.being slow in replying to your letter, which is due not so much to my deteriorating eyesight but to the undiminishing back' of my work. It is for this reason that I did not immediately reply to your earlier letter about Wei Liem and then did not follow up later. I understand that Wei Liem is doing well in his studies. Although I would have preferred him to give a seminar on my paper, I am inclined to think that the reason for his not doing so was not his weakness but rather his lack of interest in my work. I am thankful to you for the kind words you have said about my work in your manuscript on a new approach to the CLT. But I think Stein's name should be mentioned since my ideas originated from his. Etemadi's simplification of my lemma is indeed clever. Actually it is based on the same ideas that I have used but somehow had eluded me. (By the way, I did not receive your letter about Etemadi's simplification only the manuscript). Your letter which appeared in the International Herald Tribune is quite educational for those of us who are too young to experience the Second World War. It not only serves as a historical reminder but also shows the exemplary determination of your generation in the pursuit of knowledge. Today we attended a seminar on graph theory given by Paul Erd6s. But most of us found him difficult to understand because his voice was soft and his pronunciation unclear. He told us that he had cataract in one of his eyes and that his two eyes could not cooperate. We are now very busy marking examination scripts. Siegmund will not be here this year but will next year. Will you be attending the 17th Conference on Stochastic Processes and their Applications in Rome in June this year? Four of us (including myself) will be going. Will you be able to speak at our Singapore Probability Conference? We are in the process of preparing the first notice and would like to include the names of tentative speakers. Would you agree to our including your name? (We would not do so unless you agree). We will keep you informed of the development of the Conference. Please find enclosed a copy of our Conference Update. With best regards, Yours sincerely Louis H Y Chen Enc /sa Trr() AWp 4U2 SM /4# 71/M 4 VwwV pfovrW ~ g~d~ Pd v NATIONAL UNIVERSITY OF SINGAPORE MEMORANDUM F rom :.................................................................... D ep t:................................................................... Tel Ext:...................... ... ............ .... ^L <24i 7 J To:........ ................. D ep t:................................................ ............................. ......... / 4 / ^ 1) 4 '~7ee 44 i ,_. /o A14 ~t7~ ~t~Gy a~~/tc~ /8~4~~ ~i~ "4 6 q SIGAPORE PROBABILITY CONFERENCE 8 16 June 1989 Conference Update The following speakers have accepted our invitation or indicated that they would try to come: Workshop and conference speakers P. Diaconis, Harvard University E.B. Dynkin, Cornell University M.A. Pinsky, Northwestern University Conference speakers A.D. Barbour, Universitat Zirich T. Hida, Nagoya University C.R. Hwang, Academia Sirlica, Taipei H. Kesten, Cornell University S. Kotani, Kyoto University/University of Tokyo D.O. Siegmund, Stanford University C. Stein, Stanford University S. Watanabe, Kyoto University ~~7 A few invited speakers have not replied or are undecided. March 1988 y / Z17 6 ,' Received: from cornell.edu (cornell.edu [132.236.56.6]) by postoffice.mail.corne Received: from cornell.edu (PHQUERY) by cornell.edu with cornellphquery id <577 Received: from poly.math.cornell.edu ([128.84.234.31]) by cornell.edu with SMTP Received: from leonis.nus.sg by poly.math.cornell.edu (4.1/1.5) id AA10038; Wed, 20 Jul 94 06:19:20 EDT Received: from localhost (matchyl@localhost) by leonis.nus.sg (8.6.4/8.6.4/CNS2 Date: Wed, 20 Jul 1994 06:18:58 0400 XPH: V4.1@cornell.edu (Cornell Modified) From: "Louis H. Y. Chen" Sender: "Louis H. Y. Chen" ReplyTo: "Louis H. Y. Chen" Subject: Message 2 for K. L. Chung To: Rick Durrett Cc: Lou Jiann Hua MessageId: MimeVersion: 1.0 ContentType: TEXT/PLAIN; CHARSET=USASCII To Professor Kai Lai Chung c/o Professor Rick Durrett Dear Kai Lai, I hope you are enjoying your visit to Cornell. I heard that you are giving excellent lectures. I gave your problems to more colleagues (including Lou Jiann Hua) and they also solved your problem 1. As for your problem 2, Lou Jiann Hua solved it. I was at first sidetracked by thinking about the possible shapes of the open set D, but later solved the problem with some prompting from Lou. As you said, the problem is easy. One only has to consider the expected hitting time E(T) when the BM starts from a boundary point x of D for the following two cases: (1) x is regular point of the complement of the closure of D and (2) x is an irregular point of the complement of the closure of D. In the first case, T is 0 w.p.l and the expectation is 0 and therefore does not contribute to the supremum. In the second case, we let the BM move into D in an arbitrarily small length of time, and then use the strong Markov property to start from there. More precisely, E(T) = E(T; T < or = a) + E(T; T > a) < or = a + EI(T > a)E(T I B(a)) < or = a + sup E(T I B(0) = x ) where the supremum is taken over all x in D. As a > 0 is arbitrary, E(T) is no bigger than the supremum over all x in D. I hope you have time to read my previous message and agree with my proposed period of visit of 12 February 11 April 1995 (approximately). Have our written solutions to your problem 1 arrived? With best wishes. Louis '71f eut, yevised ca s5t4C 7/2 ' S, / C A e or ~~$/ /6.,e df~1 C/~f~ tU5 nz/ y L ^ 'Wat 1 O ~~C~~YP Ue~: wwt~~ D~Y j~JLlllr~ LP LIIU /UL4 p 2 < 1 e ( / E /j( m j C1 fa 1)r *fJ 8o v4 o 'k / 7 ZO " c20c. 96 AQt4 1 6;ry Pvl /2Q 7^ .~ ci~h ff c^ . ^C/MyVvv^ 7Cl) >^ Iv~^l / 1&, oA pQ~p~2~p ~h lc/ /~C4C I~R/kag V c~":~ ~~I"L~a $ILe~ Lv~ irrir (L~ Ltcdh;tZ~B rC L( 6~ VWL ~ I D2~Z)i ^^<^ ^ y^Lz^ /A^ f/~4/ ?~^r'3aBJ ~~;i~~t~~l~TI:;;t e~Y/ A) ae OK $ n In ~t L. A*IA A~ ( 1 eAe/L 6$i%^UJLsd (iCzlJ^ V2 1$2~)2/vl 3 `~CdaQ &Fie 016 ("^ tCu a4 cLtq J A I / < ^^ ^/^CK. ^ *To/oct Q 4^4 ~t~~A", pzutvve/Lg.l 1 yev'Fsec CA s5(wo 7/.2t S~ A 7 n I Q4A" ~rLL ZIcGrL7~/~ knXU4 5j ~R f/ 9 U v ^ ;4JIA ~7 6A s u f 7cfi42CsrA^ L^i dU ~~ c.~eeeee~~^<~eeeee~~~~ /2e 7f ;z~ c~/~tYI A~r '7~)ccA &d '" /V k I 7i A V iLcyvJ4h" ck 7? T^ IRQ2c 4WQ ~ / U7 C a.204, y4N Z f C' " ,P~ir 4"o )jtR c Ce Fr f LY r , fA4Jld cx)to t'gD 94&a fro 0 PDcuZc P Veer ~~ ~n4 ~ Director Dr. Louis S. Y. Chen May 1, 2004 (R at a;d) Ple hfoyIcrd ;fecess(/ Dear Louis: How are you and family'? Very busy? Hope you will visit your "campus" in MV here soon so that we can meet again) and we wnrld like to invite you. Are your children (whom we met in 1985) here? Please forward the following IMPORTANT message to your colleague Bai the famous Chinese statistician I do not know his address A and fax number and hope he is with you. Ii not please forward. Do you remember that either you or your then chairman/dean ask me to write a letter of recommendation when you wanted to invite him to your (maybe Economics ?^ department. ','e were acquainted when he was here with Ted. /itn best reet'ards and please send a fax as reply. Dear Dr. iai: C1) O Iere is a good problem !orthy of your attention. ,Aany French American and Italian prohabilists tried without success. However two ,f them and I did do half of tV e asymptotic without any use of ch. f. I am sure you can. But how about the other half? S \ OPEN Problem. et be D wih D p tk' kN e IID wih DF F. 1cpose there i s a in (01,) such that fSn/nlra for all n>l have the same distribution namely F. Prove that 1 (x) 0 x as x,oo. This is of course r.ul Levy's theorem (c. 192J). Now (I) Prove it without use of ch. f. If that is too hard, then give a. short direct proof with ch. f. T?)ere is a proof given implicitly only in the book by OnedenkoKolmororov usInr the NaYS :ffic conditions for the attraction of a DF to a stable 3?, but nobody has shown how to choose a simple F to compute the limit of the ch. f. of the normed sum to get any given stable law. Only in the symmetric case it is shown in my Course. Please reply by fax: USA S(O) 85 8 00 With kind regards, c" li) ( 5 ) ( 9 7 3 