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.