**Graduate Studies in Mathematics**

Volume: 139;
2012;
421 pp;
Hardcover

MSC: Primary 60;

Print ISBN: 978-0-8218-8532-1

Product Code: GSM/139

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-9031-8
Product Code: GSM/139.E**

List Price: $75.00

Individual Member Price: $60.00

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#### Supplemental Materials

# Knowing the Odds: An Introduction to Probability

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*John B. Walsh*

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

This 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

# Table of Contents

## Knowing the Odds: An Introduction to Probability

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Introduction xiii14 free
- Chapter 1. Probability spaces 118 free
- Chapter 2. Random variables 3956
- Chapter 3. Expectations II: The general case 7592
- Chapter 4. Convergence 117134
- Chapter 5. Laws of large numbers 133150
- Chapter 6. Convergence in distribution and the CLT 151168
- Chapter 7. Markov chains and random walks 191208
- Chapter 8. Conditional expectations 265282
- Chapter 9. Discrete-parameter martingales 275292
- Chapter 10. Brownian motion 335352
- Bibliography 413430
- Index 415432 free
- Back Cover Back Cover1439

#### Readership

Undergraduate and graduate students interested in probability theory.