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Markov Processes, Brownian Motion, and Time Symmetry (Grundlehren der mathematischen Wissenschaften) [Hardcover]

Kai Lai Chung (Author), John B. Walsh (Author)

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Book Description

July 15, 2005 0387220267 978-0387220260 2nd
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.


Editorial Reviews

Review

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. H.J. Engelbert, MathSciNet From the reviews of the second edition: "This monograph is a considerably extended second edition of K.L. Chung’s classic ‘Lectures from Markov processes to Brownian motion’ … . Adding to Chung’s masterpiece is a formidable task; the new chapters by Walsh capture the spirit of the original and give a gentle, inspiring and eminently useful introduction to Ray processes, time reversal and duality." (René L. Schilling, Zentralblatt MATH, Vol. 1082, 2006) "The volume under review is the union of two distinct, albeit complementary, works. … there are a number of interesting examples in the more familiar world of Markov chains which the reader can use to gain insight into the new ideas. … If I were asked to recommend a book to beginners who wished to immerse themselves in the subject and emerge in a fit state to tackle the contemporary literature, then I would choose this volume without hesitation." (David Applebaum, The Mathematical Gazette, Vol. 92 (523), 2008)

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Inside This Book (learn more)
First Sentence:
We begin by describing a general Markov process running on continuous time and living in a topological space. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
supermedian functions, duality hypotheses, semipolar set, hunt process, finely open set, excessive function, separability set, last exit time, fine topology, branching measure, first entrance time, superharmonic function, probabilistic potential theory, duality with respect, duality measure, ess lim, transition semigroup, positive supermartingale, continuous wherever, resolvent equation, right continuous version, compact separable metric space, fine closure, optional relative, potential kernel
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Decreasing Limits, Potential Developments, Second Look, Basic Examples, Prove Proposition, The Basis of Duality
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