**Courant Lecture Notes**

Volume: 16;
2007;
126 pp;
Softcover

MSC: Primary 60;

Print ISBN: 978-0-8218-4085-6

Product Code: CLN/16

List Price: $32.00

Individual Member Price: $25.60

**Electronic ISBN: 978-1-4704-3116-7
Product Code: CLN/16.E**

List Price: $32.00

Individual Member Price: $25.60

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#### Supplemental Materials

# Stochastic Processes

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*S. R. S. Varadhan*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

This is a brief introduction to stochastic processes studying certain
elementary continuous-time processes. After a description
of the Poisson process and related processes with independent increments
as well as a brief look at Markov processes with a
finite number of jumps, the author proceeds to introduce Brownian motion
and to develop stochastic integrals and Itô's theory in the
context of one-dimensional diffusion processes. The book ends with a
brief survey of the general theory of Markov processes.

The book is based on courses given by the author at the Courant
Institute and can be used as a sequel to the author's successful book
Probability Theory in this series.

Srinivasa S. R. Varadhan is the winner of the 2007 Abel Prize.
Varadhan was awarded the prize "for his fundamental contributions to
probability theory and
in particular for creating a unified theory of large deviations".
Read more here.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

#### Table of Contents

# Table of Contents

## Stochastic Processes

- Cover Cover11
- General Editor Information ii3
- Title page iii4
- Dedication page v6
- Contents vii8
- Preface ix10
- Introduction 112
- Processes with independent increments 1324
- Poisson point processes 2536
- Jump Markov processes 2940
- Brownian motion 4960
- One-dimensional diffusions 8798
- General theory of Markov processes 107118
- Appendix A. Measures on Polish spaces 113124
- Appendix B. Additional remarks 121132
- Bibliography 123134
- Index 125136
- Back Cover Back Cover1138

#### Readership

Graduate students and research mathematicians interested in stochastic processes.

#### Reviews

The text is one of those that may be strongly recommended to all young mathematicians as a starter to precede a deeper study of probability and stochastic processes.

-- EMS Newsletter

Amazingly, almost all of the proofs are given explicitly. In fact the author provides only eight references in the bibliography. This reflects the fact that, as a whole, this book is written in a totally self-contained manner. ...I can say that this book is a set of very well-written lecture notes, and it is organized as a clear synthesis of the theory of continuous-time stochastic processes with many examples and with plenty of exercises...

-- Mathematical Reviews