**Graduate Studies in Mathematics**

Volume: 149;
2013;
284 pp;
Hardcover

MSC: Primary 60;

Print ISBN: 978-1-4704-0907-4

Product Code: GSM/149

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-1-4704-1027-8
Product Code: GSM/149.E**

List Price: $75.00

Individual Member Price: $60.00

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#### Supplemental Materials

# Mathematics of Probability

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*Daniel W. Stroock*

This book covers the basics of modern
probability theory. It begins with probability theory on finite and
countable sample spaces and then passes from there to a concise course
on measure theory, which is followed by some initial applications to
probability theory, including independence and conditional
expectations. The second half of the book deals with Gaussian random
variables, with Markov chains, with a few continuous parameter
processes, including Brownian motion, and, finally, with martingales,
both discrete and continuous parameter ones.

The book is a self-contained introduction to probability theory and
the measure theory required to study it.

#### Table of Contents

# Table of Contents

## Mathematics of Probability

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Preface ix10 free
- Some background and preliminaries 114 free
- Probability theory on uncountable sample spaces 5568
- Some applications to probability theory 105118
- The central limit theorem and Gaussian distributions 135148
- Discrete parameter stochastic processes 159172
- Some continuous-time processes 193206
- Martingales 225238
- Notation 275288
- Bibliography 279292
- Index 281294 free
- Back Cover Back Cover1298

#### Readership

Graduate students and researchers interested in probability.

#### Reviews

... I regard this book highly, and I recommend it for course use as well as for independent study.

-- MAA Reviews

This book is a very thorough advanced undergraduate/beginning graduate course on probability theory for students who have a good background in modern mathematical ideas. ... [W]hat distinguishes this book from its many competitors is the thoroughness of argument, and the tasteful choice of auxiliary topics that complement the main menu. ... The book is replete with carefully chosen exercise for readers to test their understanding. Another nice touch is that the author always takes care to let the reader know who originally came up with a particularly clever argument or method. In this way, readers get a healthy exposure to ways of thinking originating from Doeblin, Doob, Dynkin, Huygens, Kac, Kolmogorov, Livy, Marcinkiewicz and Wiener, among many others. This is a very good book on which to base a graduate course or to use for self-study.

-- David Applebaum, University of Sheffield, South Yorkshire, UK

*Mathematics of Probability* is a very enjoyable book. It is
definitely a book for graduate students, but it manages to begin exploring the
subject without a lot of prerequisites. ... It manages to discuss rigorously,
and in a mostly self-contained manner, advanced topics which are not found in
undergraduate books. ... It is a good book for independent study. It does not
overwhelm the reader with exercises (each section ends with several problems).
The footnotes and the comments at the end of each chapter are to the point and
help the reader keep focus. ... All in all, I regard this book highly and I
recommend it for course use as well as for independent study.

-- Florin Catrina, MAA Reviews