An Introduction to Stochastic Differential Equations
Lawrence C. Evans
2012 abe. · American Mathematical Soc.
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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.
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).
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Lawrence C. Evans, University of California, Berkeley, CA, USA
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