Knowing the Odds

John B. Walsh, University of British Columbia, Vancouver, BC, Canada.

“John Walsh, one of the great masters of the subject, has written a superb book on probability. It covers at a leisurely pace all the important topics that students need to know, and provides excellent examples. I regret his book was not available when I taught such a course myself, a few years ago.” - Ioannis Karatzas, Columbia University“In this wonderful book, John Walsh presents a panoramic view of Probability Theory, starting from basic facts on mean, median and mode, continuing with an excellent account of Markov chains and martingales, and culminating with Brownian motion. Throughout, the author's personal style is apparent; he manages to combine rigor with an emphasis on the key ideas so the reader never loses sight of the forest by being surrounded by too many trees. As noted in the preface, ""To teach a course with pleasure, one should learn at the same time."" Indeed, almost all instructors will learn something new from the book (e.g. the potential-theoretic proof of Skorokhod embedding) and at the same time, it is attractive and approachable for students.” - Yuval Peres, Microsoft“With many examples in each section that enhance the presentation, this book is a welcome addition to the collection of books that serve the needs of advanced undergraduate as well as first year graduate students. The pace is leisurely which makes it more attractive as a text.” - Srinivasa Varadhan, Courant Institute, New York

• Probability spacesRandom variablesExpectations II: The general caseConvergenceLaws of large numbersConvergence in distribution and the CLTMarkov chains and random walksConditional expectationsDiscrete-parameter martingalesBrownian motionBibliographyIndex