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).
General
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