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Elementary Probability Theory with Stochastic Processes
This book provides an elementary introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. The fourth edition adds material related to mathematical finance, as well as expansions on stable laws and martingales.
A Course in Probability Theory
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.
Elementary Probability Theory
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
Markov Chains with Stationary Transition Probabilities
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 bo...
Markov Processes, Brownian Motion, and Time Symmetry
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.
From Brownian Motion to Schrödinger’s Equation
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.
A Course in Probability Theory
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.
Introduction to Random Time and Quantum Randomness
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.
Introduction to Stochastic Integration
A highly readable introduction to stochastic integration and stochastic differential equations, this book combines developments of the basic theory with applications. It is written in a style suitable for the text of a graduate course in stochastic calculus, following a course in probability. Using the modern approach, the stochastic integral is defined for predictable integrands and local martingales; then It’s change of variable formula is developed for continuous martingales. Applications include a characterization of Brownian motion, Hermite polynomials of martingales, the Feynman–Kac functional and the Schrödinger equation. For Brownian motion, the topics of local time, reflected B...
