2013;
151 pp;
Softcover

MSC: Primary 65; 60;

Print ISBN: 978-1-4704-1054-4

Product Code: MBK/82

List Price: $34.00

AMS Member Price: $27.20

MAA member Price: $30.60

**Electronic ISBN: 978-1-4704-1612-6
Product Code: MBK/82.E**

List Price: $34.00

AMS Member Price: $27.20

MAA member Price: $30.60

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#### Supplemental Materials

# An Introduction to Stochastic Differential Equations

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*Lawrence C. Evans*

These notes provide a concise introduction to stochastic differential equations and their application to the study of financial markets and as a basis for modeling diverse physical phenomena. They are accessible to non-specialists and make a valuable addition to the collection of texts on the topic.

—Srinivasa Varadhan, New York University

This is a handy and very useful text for studying stochastic differential equations. There is enough mathematical detail so that the reader can benefit from this introduction with only a basic background in mathematical analysis and probability.

—George Papanicolaou, Stanford University

This book covers the most important elementary facts regarding stochastic differential equations; it also describes some of the applications to partial differential equations, optimal stopping, and options pricing. The book's style is intuitive rather than formal, and emphasis is made on clarity. This book will be very helpful to starting graduate students and strong undergraduates as well as to others who want to gain knowledge of stochastic differential equations. I recommend this book enthusiastically.

—Alexander Lipton, Mathematical Finance
Executive, Bank of America Merrill Lynch

This short book provides a quick, but very readable introduction to
stochastic differential equations, that is, to differential equations
subject to additive “white noise” and related random disturbances.
The exposition is concise and strongly focused upon the interplay
between probabilistic intuition and mathematical rigor. Topics include
a quick survey of measure theoretic probability theory, followed by an
introduction to Brownian motion and the Itô stochastic calculus, and
finally the theory of stochastic differential equations. The text also
includes applications to partial differential equations, optimal
stopping problems and options pricing.

This book can be used as a text for senior undergraduates or
beginning graduate students in mathematics, applied mathematics,
physics, financial mathematics, etc., who want to learn the basics of
stochastic differential equations. The reader is assumed to be fairly
familiar with measure theoretic mathematical analysis, but is not
assumed to have any particular knowledge of probability theory (which
is rapidly developed in Chapter 2 of the book).

#### Readership

Undergraduate and graduate students interested in probability theory and stochastic differential equations.

#### Reviews & Endorsements

... [A]n interesting and unusual introduction to stochastic differential equations...topical and appealing to a wide audience. ... This is interesting stuff and, because of Evans' always clear explanations, it is fun too.

-- MAA Reviews

#### Table of Contents

# Table of Contents

## An Introduction to Stochastic Differential Equations

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Introduction 110 free
- A crash course in probability theory 716 free
- Brownian motion and “white noise” 3746
- Stochastical integrals 5968
- Stochastic differential equations 8392
- Applications 103112
- Appendix 127136
- Exercises 135144
- Notes and suggested reading 145154
- Bibliography 147156
- Index 149158 free
- Back Cover Back Cover1161