Kai Lai Chung's Books

Selected Works of Kai Lai Chung

By: Kai Lai Chung,Farid AitSahlia

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Selected Works of Kai Lai Chung

By: Kai Lai Chung,Farid AitSahlia

This unique volume presents a collection of the extensive journal publications written by Kai Lai Chung over a span of 70-odd years. It was produced to celebrate his 90th birthday. The selection is only a subset of the many contributions that he 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.As Kai Lai Chung's contributions spawned critical new developments, this volume also contains retrospective and perspective views provided by collaborators and other authors who themselves advanced the areas of probability and mathematics.

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Page Count

847

Publisher

World Scientific

Published Date

ISBN 10

9812833854

ISBN 13

9789812833853

A Course in Probability Theory

By: Kai Lai Chung

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A Course in Probability Theory

By: Kai Lai Chung

This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a "must", although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.

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Page Count

381

Publisher

Academic Press

Published Date

ISBN 10

0080570402

ISBN 13

9780080570402

Introduction To Random Time And Quantum Randomness (New Edition)

By: Kai Lai Chung,Jean-claude Zambrini

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Introduction To Random Time And Quantum Randomness (New Edition)

By: Kai Lai Chung,Jean-claude Zambrini

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.

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Page Count

225

Publisher

World Scientific

Published Date

ISBN 10

9814485861

ISBN 13

9789814485869

A Course in Probability Theory

By: Kai Lai Chung

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A Course in Probability Theory

By: Kai Lai Chung

Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.

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Page Count

440

Publisher

Academic Press

Published Date

ISBN 10

0121741516

ISBN 13

9780121741518

Elementary Probability Theory

With Stochastic Processes and an Introduction to Mathematical Finance

By: Kai Lai Chung,Farid AitSahlia

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Elementary Probability Theory

With Stochastic Processes and an Introduction to Mathematical Finance

By: Kai Lai Chung,Farid AitSahlia

This book provides an introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales. From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS

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Page Count

411

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387215484

ISBN 13

9780387215488

Chance & Choice

Memorabilia

By: Kai Lai Chung

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Chance & Choice

Memorabilia

By: Kai Lai Chung

This book begins with a historical essay entitled OC Will the Sun Rise Again?OCO and ends with a general address entitled OC Mathematics and ApplicationsOCO. The articles cover an interesting range of topics: combinatoric probabilities, classical limit theorems, Markov chains and processes, potential theory, Brownian motion, SchrAdingerOCoFeynman 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 book. Contents: On Mutually Favorable Events; On Fluctuations in Coin-Tossing; On a Stochastic Approximation Method; On the Martin Boundary for Markov Chains; A Cluster of Great Formulas; Probabilistic Methods in Markov Chains; Markov Processes with Infinities; Probability Methods in Potential Theory; Plya''s Work in Probability; Probability and Doob; In Memory of L(r)vy and Fr(r)chet; and other papers. Readership: Graduate students, teachers and researchers in probability and statistics.

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Page Count

344

Publisher

World Scientific

Published Date

ISBN 10

9812567135

ISBN 13

9789812567130

Green, Brown, and Probability

By: Kai Lai Chung

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Green, Brown, and Probability

By: Kai Lai Chung

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.

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Page Count

124

Publisher

World Scientific

Published Date

ISBN 10

9810225334

ISBN 13

9789810225339

Markov Processes, Brownian Motion, and Time Symmetry

By: Kai Lai Chung,John B. Walsh

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Markov Processes, Brownian Motion, and Time Symmetry

By: Kai Lai Chung,John B. Walsh

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.

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Page Count

444

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387286969

ISBN 13

9780387286969

From Brownian Motion to Schrödinger’s Equation

By: Kai L. Chung,Zhongxin Zhao

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From Brownian Motion to Schrödinger’s Equation

By: Kai L. Chung,Zhongxin Zhao

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.

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Page Count

297

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364257856X

ISBN 13

9783642578564

Markov Chains with Stationary Transition Probabilities

By: Kai Lai Chung

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Markov Chains with Stationary Transition Probabilities

By: Kai Lai Chung

The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools.

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Page Count

287

Publisher

Springer

Published Date

ISBN 10

3642496865

ISBN 13

9783642496868

Elementary Probability Theory

With Stochastic Processes and an Introduction to Mathematical Finance

By: K. L. Chung,Farid AitSahlia

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Elementary Probability Theory

With Stochastic Processes and an Introduction to Mathematical Finance

By: K. L. Chung,Farid AitSahlia

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Page Count

432

Publisher

Springer Science & Business Media

Published Date

ISBN 10

038795578X

ISBN 13

9780387955780

Emotional Capitalism

From Emotional Dictatorship to Emotional Redemption

By: Peter Wing-Kai Lok

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Emotional Capitalism

From Emotional Dictatorship to Emotional Redemption

By: Peter Wing-Kai Lok

As today's emotional capitalism increasingly carries out its core operation of regulating the psycho-energy of individuals, the need to analyse a variety of methods for emotional production becomes important. By bringing together the works of Byung-Chul Han, Bernard Stiegler, Emmanuel Levinas, and Judith Butler, this bold analysis offers a fresh perspective on the operation of emotional capitalism today, with various possibilities for evolving a sensitivity to social injustice and the suffering of others through an ethical, affective, and bodily inter-subjective connection.

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Page Count

130

Publisher

John Hunt Publishing

Published Date

ISBN 10

1803414510

ISBN 13

9781803414515

Green, Brown, and Probability & Brownian Motion on the Line

By: Kai Lai Chung

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Green, Brown, and Probability & Brownian Motion on the Line

By: Kai Lai Chung

This invaluable book consists of two parts. Part I is the second edition of the author's widely acclaimed publication Green, Brown, and Probability, which first appeared in 1995. In this exposition the author reveals, from a historical perspective, the beautiful relations between the Brownian motion process in probability theory and two important aspects of the theory of partial differential equations initiated from the problems in electricity ? Green's formula for solving the boundary value problem of Laplace equations and the Newton-Coulomb potential.Part II of the book comprises lecture notes based on a short course on ?Brownian Motion on the Line? which the author has given to graduate students at Stanford University. It emphasizes the methodology of Brownian motion in the relatively simple case of one-dimensional space. Numerous exercises are included.

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Page Count

184

Publisher

World Scientific

Published Date

ISBN 10

9810246900

ISBN 13

9789810246907

Lectures from Markov Processes to Brownian Motion

By: Kai Lai Chung

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Lectures from Markov Processes to Brownian Motion

By: Kai Lai Chung

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 § 1. 4. Apart from this and some dispensable references to Markov chains as examples, the book is self-contained.

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Page Count

248

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475717768

ISBN 13

9781475717761

Green, Brown, And Probability And Brownian Motion On The Line

By: Kai Lai Chung

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Green, Brown, And Probability And Brownian Motion On The Line

By: Kai Lai Chung

This invaluable book consists of two parts. Part I is the second edition of the author's widely acclaimed publication Green, Brown, and Probability, which first appeared in 1995. In this exposition the author reveals, from a historical perspective, the beautiful relations between the Brownian motion process in probability theory and two important aspects of the theory of partial differential equations initiated from the problems in electricity — Green's formula for solving the boundary value problem of Laplace equations and the Newton-Coulomb potential.Part II of the book comprises lecture notes based on a short course on “Brownian Motion on the Line” which the author has given to graduate students at Stanford University. It emphasizes the methodology of Brownian motion in the relatively simple case of one-dimensional space. Numerous exercises are included.

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Page Count

188

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813102527

ISBN 13

9789813102521

Chance & Choice

Memorabilia

By: Kai Lai Chung

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Chance & Choice

Memorabilia

By: Kai Lai Chung

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 book.

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