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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Brownian Motion, Martingales, and Stochastic Calculus (Hardcover, 1st ed. 2016)
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Brownian Motion, Martingales, and Stochastic Calculus (Hardcover, 1st ed. 2016)
Series: Graduate Texts in Mathematics, 274
Expected to ship within 10 - 15 working days
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This book offers a rigorous and self-contained presentation of
stochastic integration and stochastic calculus within the general
framework of continuous semimartingales. The main tools of
stochastic calculus, including Ito's formula, the optional stopping
theorem and Girsanov's theorem, are treated in detail alongside
many illustrative examples. The book also contains an introduction
to Markov processes, with applications to solutions of stochastic
differential equations and to connections between Brownian motion
and partial differential equations. The theory of local times of
semimartingales is discussed in the last chapter. Since its
invention by Ito, stochastic calculus has proven to be one of the
most important techniques of modern probability theory, and has
been used in the most recent theoretical advances as well as in
applications to other fields such as mathematical finance. Brownian
Motion, Martingales, and Stochastic Calculus provides a strong
theoretical background to the reader interested in such
developments. Beginning graduate or advanced undergraduate students
will benefit from this detailed approach to an essential area of
probability theory. The emphasis is on concise and efficient
presentation, without any concession to mathematical rigor. The
material has been taught by the author for several years in
graduate courses at two of the most prestigious French
universities. The fact that proofs are given with full details
makes the book particularly suitable for self-study. The numerous
exercises help the reader to get acquainted with the tools of
stochastic calculus.
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