**Graduate Studies in Mathematics**

Volume: 113;
2010;
271 pp;
Hardcover

MSC: Primary 60;
Secondary 35

Print ISBN: 978-0-8218-4949-1

Product Code: GSM/113

List Price: $58.00

Individual Member Price: $46.40

**Electronic ISBN: 978-1-4704-1175-6
Product Code: GSM/113.E**

List Price: $58.00

Individual Member Price: $46.40

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#### Supplemental Materials

# Continuous Time Markov Processes: An Introduction

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*Thomas M. Liggett*

Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example—one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology.

This is a textbook for a graduate course that can follow one that covers basic probabilistic limit theorems and discrete time processes.

#### Table of Contents

# Table of Contents

## Continuous Time Markov Processes: An Introduction

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface ix10 free
- One-dimensional Brownian motion 114 free
- Continuous time Markov chains 5770
- Feller processes 91104
- Interacting particle systems 133146
- Stochastic integration 193206
- Multidimensional Brownian motion and the Dirichlet problem 227240
- Appendix 247260
- Bibliography 267280
- Index 269282 free
- Back Cover Back Cover1288

#### Readership

Graduate students and research mathematicians interested in probability.