WorldCat Identities

Chung, Kai Lai 1917-2009

Overview
Works: 91 works in 713 publications in 6 languages and 17,091 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Editor, Other, Translator, Author of introduction, ed
Classifications: QA273, 519.2
Publication Timeline
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Most widely held works about Kai Lai Chung
 
Most widely held works by Kai Lai Chung
Elementary probability theory with stochastic processes by Kai Lai Chung( Book )

74 editions published between 1974 and 2003 in 4 languages and held by 1,471 WorldCat member libraries worldwide

Set; Probability; Couting; Random variables; Conditioning and independence; Mean, variance and transforms; Poisson and normal distribution; From Random walks to markov chains
A course in probability theory by Kai Lai Chung( Book )

61 editions published between 1968 and 2011 in 3 languages and held by 1,338 WorldCat member libraries worldwide

Distribution function; Measure theory; Random variable. Expectation. Independence; Convergence concepts; Law of large numbers. Random series; Characteristic function; Central limit theorem and its ramifications; Random walk; Conditioning. Markov property. Martingale
Markov chains with stationary transition probabilities by Kai Lai Chung( Book )

47 editions published between 1960 and 2013 in 3 languages and held by 998 WorldCat member libraries worldwide

"This book presupposes no knowledge of Markov chains but it does assume the elements of general probability theory as given in a modern introductory course."--Preface
Introduction to stochastic integration by Kai Lai Chung( Book )

54 editions published between 1983 and 2014 in 6 languages and held by 765 WorldCat member libraries worldwide

The contents of this monograph approximate the lectures I gave In a graduate course at Stanford University in the first half of 1981. But the material has been thoroughly reorganized and rewritten. The purpose is to present a modern version of the theory of stochastic in tegration, comprising but going beyond the classical theory, yet stopping short of the latest discontinuous (and to some distracting) ramifications. Roundly speaking, integration with respect to a local martingale with continuous paths is the primary object of study here. We have decided to include some results requiring only right continuity of paths, in order to illustrate the general methodology. But it is possible for the reader to skip these extensions without feeling lost in a wilderness of generalities. Basic probability theory inclusive of martingales is reviewed in Chapter 1. A suitably prepared reader should begin with Chapter 2 and consult Chapter 1 only when needed. Occasionally theorems are stated without proof but the treatmcnt is aimed at self-containment modulo the in evitable prerequisites. With considerable regret I have decided to omit a discussion of stochastic differential equations. Instead, some other ap plications of the stochastic calculus are given; in particular Brownian local time is treated in dctail to fill an unapparent gap in the literature. x I PREFACE The applications to storage theory discussed in Section 8. 4 are based on lectures given by J. Michael Harrison in my class
Lectures from Markov processes to Brownian motion by Kai Lai Chung( Book )

17 editions published between 1981 and 1982 in English and held by 497 WorldCat member libraries worldwide

This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism.) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book as the Course, and may be considered as a general background; its specific use is limited to the mate rial on discrete parameter martingale theory cited in {sect} 1. 4. Apart from this and some dispensable references to Markov chains as examples, the book is self-contained
Lectures on boundary theory for Markov chains by Kai Lai Chung( Book )

20 editions published between 1968 and 1971 in English and held by 485 WorldCat member libraries worldwide

The boundary theory as viewed in this book is a study of Markov chains with certain infinities (discontinuities that are not jumps) in the sample functions. In the first part a simple 'boundary' is set up by a direct, intuitive method and the basic relevant sample behavior is studied. The second, more substantial part of this book deals with the analysis of the chain in relation to its menimal part and its exits and entrances to and from the boundary. (Author)
From Brownian motion to Schrödinger's Equation by Kai Lai Chung( Book )

21 editions published between 1995 and 2001 in English and held by 433 WorldCat member libraries worldwide

In recent years, the study of the theory of Brownian motion has become a powerful tool in the solution of problems in mathematical physics. This self-contained and readable exposition by leading authors, provides a rigorous account of the subject, emphasizing the "explicit" rather than the "concise" where necessary, and addressed to readers interested in probability theory as applied to analysis and mathematical physics. A distinctive feature of the methods used is the ubiquitous appearance of stopping time. The book contains much original research by the authors (some of which published here for the first time) as well as detailed and improved versions of relevant important results by other authors, not easily accessible in existing literature
Elementary probability theory : with stochastic processes and an introduction to mathematical finance by Kai Lai Chung( Book )

20 editions published between 2003 and 2010 in English and Undetermined and held by 397 WorldCat member libraries worldwide

This is a fourth edition of a classic reference on probability theory. Among the numerous introductions to the subject, this one covers a wide range of topics. For this edition, two chapters have been added on mathematical finance
Markov processes, Brownian motion, and time symmetry by Kai Lai Chung( Book )

34 editions published between 2004 and 2013 in English and Spanish and held by 295 WorldCat member libraries worldwide

From the reviews of the First Edition: "This excellent book is based on several sets of lecture notes written over a decade and has its origin in a one-semester course given by the author at the ETH, Zürich, in the spring of 1970. The author's aim was to present some of the best features of Markov processes and, in particular, of Brownian motion with a minimum of prerequisites and technicalities. The reader who becomes acquainted with the volume cannot but agree with the reviewer that the author was very successful in accomplishing this goal...The volume is very useful for people who wish to learn Markov processes but it seems to the reviewer that it is also of great interest to specialists in this area who could derive much stimulus from it. One can be convinced that it will receive wide circulation." (Mathematical Reviews) This new edition contains 9 new chapters which include new exercises, references, and multiple corrections throughout the original text
Green, Brown, and probability & Brownian motion on the line by Kai Lai Chung( Book )

20 editions published in 2002 in English and held by 258 WorldCat member libraries worldwide

Pao-Lu Hsü collected papers by Baolu Xu( Book )

9 editions published between 1982 and 1983 in English and held by 239 WorldCat member libraries worldwide

Green, Brown, and probability by Kai Lai Chung( Book )

15 editions published between 1995 and 2002 in English and held by 208 WorldCat member libraries worldwide

This volume shows modern probabilistic methods in action: Brownian Motion Process as applied to the electrical phenomena investigated by Green et al., beginning with the Newton-Coulomb potential and ending with solutions by first and last exits of Brownian paths from conductors
Four papers on probability by Kai Lai Chung( Book )

21 editions published between 1951 and 1971 in 3 languages and held by 179 WorldCat member libraries worldwide

Seminar on Stochastic Processes, 1981 by E Çınlar( Book )

17 editions published between 1981 and 1988 in English and Undetermined and held by 174 WorldCat member libraries worldwide

This volume consists of about half of the papers presented during a three-day seminar on stochastic processes held at Northwestern University in April 1981. The aim of the seminar was to bring together a small group of kindred spirits working on stochastic processes and to provide an informal atmosphere for them to discuss their current work. We plan to hold such a seminar once a year, with slight variations in emphasis to reflect the changing concerns and interests within the field. The invited participants in this year's seminar were J. AZEMA, R.M. BLUMENTHAL, R. CARMONA, K.L. CHUNG, R.K. GETOOR, J. JACOD, F. KNIGHT, S. OREY, A.O. PITTENGER, J. PITMAN, P. PROTTER, M.K. RAO, M. SHARPE, and J. WALSH. We thank them and other participants for the productive liveliness of the seminar. As mentioned above, the present volume is only a fragment of the work discussed at the seminar, the other papers having been already committed to otherpublications. The seminar was made possible through the enlightened support of the Air Force Office of Scientific Research, Grant No. 80-0252. We are grateful to them as well as the publisher, Birkhauser Boston, for their support and encouragement
Chance & choice : memorabilia by Kai Lai Chung( Book )

20 editions published between 2004 and 2005 in English and Undetermined and held by 169 WorldCat member libraries worldwide

This book begins with a historical essay entitled "Will the Sun Rise Again?" and ends with a general address entitled "Mathematics and Applications". The articles cover an interesting range of topics: combinatoric probabilities, classical limit theorems, Markov chains and processes, potential theory, Brownian motion, Schrödinger-Feynman problems, etc. They include many addresses presented at international conferences and special seminars, as well as memorials to and reminiscences of prominent contemporary mathematicians and reviews of their works. Rare old photos of many of them enliven the bo
Introduction to random time and quantum randomness by Kai Lai Chung( Book )

26 editions published between 2001 and 2003 in English and Undetermined and held by 169 WorldCat member libraries worldwide

This book is made up of two essays on the role of time in probability and quantum physics. In the first one, K.L. Chung explains why, in his view, probability theory starts where random time appears. This idea is illustrated in various probability schemes and the deep impact of those random times on the theory of the stochastic process is shown. In the second essay J.-C. Zambrini shows why quantum physics is not a regular probabilistic theory, but also why stochastic analysis provides new tools for analyzing further the meaning of Feynman's path integral approach and a number of foundational issues of quantum physics far beyond what is generally considered. The role of the time parameter, in this theory, is critically re-examined and a fresh way to approach the long-standing problem of the quantum time observable is suggested
Seminar on Stochastic Processes, 1982 by Seminar on Stochastic Processes( Book )

12 editions published in 1983 in English and Undetermined and held by 147 WorldCat member libraries worldwide

This volume consists of about half of the papers presented during a three-day seminar on stochastic processes held at Northwestern University in March 1982. This was the second of such yearly seminars aimed at bringing together a small group of researchers to discuss their current work in an informal atmosphere. The invited participants in this year's seminar were B. ATKINSON, R. BASS, K. BICHTELER, D. BURKHOLDER, K.L. CHUNG, J.L. DOOB, C. DOLEANS-DADE, H. FOLLMER, R.K. GETOOR, J. GLOVER, J. MITRO, D. MONRAD, E. PERKINS, J. PITMAN, Z. POP-STOJANOVIC, M.J. SHARPE, and J. WALSH. We thank them and the other participants for the lively atmosphere of the seminar. As mentioned above, the present volume is only a fragment of the work discussed at the seminar, the other work having been committed to other publications. The seminar was made possible through the enlightened support of the Air Force Office of Scientific Research, Grant No. 80-0252A. We are grateful to them as well as the publisher, Birkhauser, Boston, for their support and encouragement. E.C., Evanston, 1983 Seminar on stochastic Processes, 1982 Birkhauser, Boston, 1983 GERM FIELDS AND A CONVERSE TO THE STRONG MARKOV PROPERTY by BRUCE W. ATKINSON 1. Introduction The purpose of this paper is to give an intrinsic characterization of optional (i.e., stopping) times for the general germ Markov process, which includes the general right process as a special case. We proceed from the general to the specific
Seminar on Stochastic Processes, 1983 by E Çınlar( Book )

13 editions published between 1984 and 1986 in English and Undetermined and held by 144 WorldCat member libraries worldwide

This volume consists of about half of the papers presented during a three-day seminar on stochastic processes. The seminar was the third of such yearly seminars aimed at bringing together a small group of researchers to discuss their current work in an informal atmosphere. The previous two seminars were held at Northwesterr. University, Evanston. This one was held at the University of Florida, Gainesville. The invited participants in the seminar were B. ATKINSON, K.L. CHUNG, C. DELLACHERIE, J.L. DOOB, E.B. DYNKIN, N. FALKNER, R.K. GETOOR, J. GLOVER, T. JEULIN, H. KASPI, T. McCONNELL, J. MITRO, E. PERKINS, Z. POP-STOJANOVIC, M. RAO, L.C.G. ROGERS, P. SALMINEN, M.J. SHARPE, S.R.S. VARADHAN, and J. WALSH. We thank them and the other participants for the lively atmosphere they have created. The seminar was made possible through the generous supports of the University of Florida, Department of Mathematics, and the Air Force Office of Scientific Research, Grant No. 82-0189, to Northwestern University. We are grateful for their support. Finally, we thank Professors Zoran POP-STOJANOVIC and Murali RAO for their time, effort, and kind hospitality in the organization of the seminar and during our stay in Gainesville
Seminar on Stochastic Processes, 1984 by E Çınlar( Book )

14 editions published between 1985 and 1986 in English and Undetermined and held by 136 WorldCat member libraries worldwide

This volume consists of about half of the papers presented during a three-day seminar on stochastic processes held at Northwestern U- versity, Evanston. The seminar was the fourth of such yearly seminars aimed at bringing together a small group of researchers to discuss their current work in an informal atmosphere. The invited participants in the seminar were B.W. ATKINSON, R.M. BLUMENTHAL, K. BURDZY, D. BURKHOLDER, M. CRANSTON, C. DOLEANS"'DADE, J.L. DOOB, N. FALKNER, P. FITZSIMMONS, J. GLOVER, F. KNIGHT, T. McCONNELL, J.B. MITRO, S. OREY, J. PITMAN, A.O. PITTENGER, Z. POP- STOJANOVIC, P. PROTTER, T. SALISBURY, M. SHARPE, C.T. SHIH, A. SZNITMAN, S.J. TAYLOR, J. WALSH, and R. WILLIAMS. We thank them and the other partiCipants for the lively seminar they created. The seminar was made possible through the partial support of the Air Force Office of Scientific Research via their Grant No. 82-0109 to Northwestern University. E
Selected works of Kai Lai Chung by Kai Lai Chung( Book )

11 editions published in 2008 in English and Undetermined and held by 77 WorldCat member libraries worldwide

This unique volume presents a collection of the extensive journal publications written by Kai Lai Chung over a span of 70-odd years. It is produced to celebrate his 90th birthday. The selection is only a subset of the many contributions that he has made throughout his prolific career. Another volume, Chance and Choice, published by World Scientific in 2004, contains yet another subset, with four articles in common with this volume. Kai Lai Chung's research contributions have had a major influence on several areas in probability. Among his most significant works are those related to sums of independent random variables, Markov chains, time reversal of Markov processes, probabilistic potential theory, Brownian excursions, and gauge theorems for the Schrdinger equation
 
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Lectures on boundary theory for Markov chains
Alternative Names
Chung, K. 1917-2009

Chung, K.L.

Chung K. L. 1917-....

Chung, K.L. 1917-2009

Chung, K. L. (Kai Lai), 1917-

Chung, K. L. (Kai Lai), 1917-2009

Chung, Kai 1917-2009

Chung, Kai L.

Chung, Kai L. 1917-2009

Chung, Kai Lai

Chung Kai Lai 1917-....

Chung, Kai-Lai 1917-2009

Chung Kai-lai American mathematician

Chung Kai-lai Amerikaans wiskundige (1917-2009)

Chung Kai-lai amerikansk matematikar

Chung Kai-lai amerikansk matematiker

Chung Kai-lai matemàtic estatunidenc

Chung Kai-lai matemático estadounidense

Chung Kai-lai matematico statunitense

Chung Kai-lai mathématicien américain

Chung, Kailai

Chzhun, Kaĭ-laĭ 1917-2009

Čžun, K.

Čžun, K. 1917-2009

Čžun, Kaj-laj.

Kai Lai Chung.

Kai Lai, Chung 1917-

Kai, Lai Chung 1917-2009

Kai Lai Chung US-amerikanischer Mathematiker

Kailai, Zhong 1917-

Zhong Kai Lai 1917-....

Zhong, Kailai

Zhong, Kailai 1917-

Чжун, К 1917-2009

Чжун, К. (Кай Лай), 1917-2009

Чжун, К. Л 1917-2009

Чжун, К. Л. (Кай Лай), 1917-2009

锺 開 萊 1917-....

钟开莱 美国数学家

Languages
English (466)

German (16)

Russian (10)

Chinese (4)

Italian (4)

Spanish (1)

Covers
A course in probability theoryMarkov chains with stationary transition probabilitiesIntroduction to stochastic integrationLectures on boundary theory for Markov chainsFrom Brownian motion to Schrödinger's EquationElementary probability theory : with stochastic processes and an introduction to mathematical financeMarkov processes, Brownian motion, and time symmetryGreen, Brown, and probability & Brownian motion on the line