An Introduction to Stochastic Differential Equations (Monograph Books) - Softcover

Evans, Lawrence C.

Softcover

ISBN 10: 1470410540 ISBN 13: 9781470410544

Publisher: American Mathematical Society, 2013

Synopsis

This 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 strongly focused upon the interplay between probabilistic intuition and mathematical rigour. Topics include a quick survey of measure theoretic probability theory, followed by an introduction to Brownian motion and the Ito 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).

About this title

Review

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

“... [A]n interesting and unusual introduction to stochastic differential equations...topical and appealing to a wide audience. ... This is interesting stuff and, because of Evan’s always clear explanations, it is fun too.”
-- MAA

About the Author

Lawrence C. Evans, University of California, Berkeley, CA, USA

Edition details

• Publisher: American Mathematical Society
• Publication date: 2013
• ISBN 10: 1470410540
• ISBN 13: 9781470410544
• Binding: Paperback
• Language: English
• Number of pages: 151