**Graduate Studies in Mathematics**

Volume: 80;
2007;
224 pp;
Hardcover

MSC: Primary 60;
Secondary 28

Print ISBN: 978-0-8218-4215-7

Product Code: GSM/80

List Price: $49.00

AMS Member Price: $39.20

MAA Member Price: $44.10

**Electronic ISBN: 978-1-4704-1157-2
Product Code: GSM/80.E**

List Price: $49.00

AMS Member Price: $39.20

MAA Member Price: $44.10

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# Probability

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*Davar Khoshnevisan*

This is a textbook for a one-semester graduate
course in measure-theoretic probability theory, but with ample
material to cover an ordinary year-long course at a more leisurely
pace. Khoshnevisan's approach is to develop the ideas that are
absolutely central to modern probability theory, and to showcase them
by presenting their various applications. As a result, a few of the
familiar topics are replaced by interesting non-standard ones.

The topics range from undergraduate probability and classical limit
theorems to Brownian motion and elements of stochastic calculus.
Throughout, the reader will find many exciting applications of
probability theory and probabilistic reasoning. There are numerous
exercises, ranging from the routine to the very difficult. Each chapter
concludes with historical notes.

#### Readership

Graduate students interested in probability theory.

#### Reviews & Endorsements

...overall the text is neatly written and presents not only good mathematics but also a heuristic view of modern probability, including numerous exercises and historical notes.

-- European Mathematical Society Newsletter

#### Table of Contents

# Table of Contents

## Probability

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents vii8 free
- Preface xi12 free
- General Notation xv16 free
- Chapter 1. Classical Probability 118 free
- Chapter 2. Bernoulli Trials 1734
- Chapter 3. Measure Theory 2340
- Chapter 4. Integration 3552
- Chapter 5. Product Spaces 5370
- Chapter 6. Independence 6582
- Chapter 7. The Central Limit Theorem 91108
- Chapter 8. Martingales 119136
- Chapter 9. Brownian Motion 159176
- Chapter 10. Terminus: Stochastic Integration 181198
- Appendix 203220
- Bibliography 209226
- Index 217234
- Back Cover Back Cover1242