An Introduction to Stochastic Differential Equations

Lawrence C. Evans (Author)

9781470410544

Hardback, published 30 January 2014

151 pages
25.6 x 18 x 1.4 cm, 0.295 kg

... [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

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).

• Preface
• Introduction
• A crash course in probability theory
• Brownian motion and “
  white noise”
  
• Stochastical integrals
• Stochastic differential equations
• Applications
• Appendix
• Exercises
• Notes and suggested reading
• Bibliography
• Index