Knowing the Odds

John B. Walsh

• Publisher: American Mathematical Society
• Year: 2012
• Print ISBN:
  9781470473877
• eBook ISBN:
  9780821890318
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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 UniversityIn 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, MicrosoftWith 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 YorkThis book covers in a leisurely manner all the standard material that one would want in a full year probability course with a slant towards applications in financial analysis at the graduate or senior undergraduate honors level. It contains a fair amount of measure theory and real analysis built in but it introduces sigma-fields, measure theory, and expectation in an especially elementary and intuitive way. A large variety of examples and exercises in each chapter enrich the presentation in the text.

Table of contents

• Front Cover: Knowing the Odds
• Half Title: Knowing the Odds
• Title: Knowing the Odds: An Introduction to Probability
• Copyright page
• Dedication
• Contents
• Preface
• Introduction
• Chapter 1: Probability Spaces
• Chapter 2: Random Variables
• Chapter 3: Expectations II: The General Case
• Chapter 4: Convergence
• Chapter 5: Laws of Large Numbers
• Chapter 6: Convergence in Distribution and the CLT
• Chapter 7: Markov Chains and Random Walks
• Chapter 8: Conditional Expectations
• Chapter 9: Discrete-Parameter Martingales
• Chapter 10: Brownian Motion
• Bibliography
• Index
• Back Cover