Synopsis
Students and teachers of mathematics and related fields will find in this second edition, as previously, a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra.Revisions and additions to the second edition:* A variety of applications?Bayesian statistics, financial mathematics, information theory, tomography, and signal processing?appear as threads in conjunction with the relevant mathematics. The goal is to both enhance the understanding of the mathematics and motivate students whose main interests are outside of pure areas.* The relevant measure theory is integrated with the standard topics of probability theory. The latter part of the book examines stochastic processes in both discrete and continuous time: martingales, renewal sequences, Markov processes, exchangeable sequences, stationary sequences, point processes, diffusions, and stochastic calculus. The treatment of stochastic calculus has been expanded considerably.* Numerous examples illustrate the richness and variety of the subject, from sophisticated results in gambling theory to concrete calculations involving random sets.* Over 1,000 exercises are designed to give a deep intuitive feel for the far-reaching implications of the theory.* A solutions manual is available, containing information for about 30 per cent of the exercises, ranging from a simple answer in some cases to a full-detailed calculation with accompanying proofs in others.
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Review
"Covers the essentials in a clear and readable fashion… A must for professionals and an attractive text for a graduate course." —American Mathematical Monthly (review of the first edition) "This ambitious book is intended as ‘a textbook in probability for graduate students in mathematics and related areas such as economics, statistics, physics and operations research’…The coverage is careful and thorough…Quite a lot of fairly recent material is incorporated, and this is certainly one of the book’s strengths. The selection of material is sensible, and the quality of exposition is good…In sum: the book contains a lot of good mathematics, nicely done, and should prove useful to students and teachers, and to specialists in probability theory." —Mathematical Reviews (review of the first edition) "The book takes the reader from a relatively low level.... To the point where he or she can specialize in research topics of current interest. ...an outstanding basis for teaching a graduate course in probability theory. The exhaustive compilation of results and detailed index also make it a very useful reference text for the more advanced probabilist... a good buy for anyone looking for a very accessible and complete mathematical account of modern probability theory." —Journal of the American Statistical Association (review of the first edition)
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