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Brownian Motion, Martingales, and Stochastic Calculus (Graduate Texts in Mathematics)

Amazon.com Price: $55.99 (as of 01/05/2019 13:20 PST- Details)

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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 Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also comprises 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 Itô, stochastic calculus has proven to be one of the vital important techniques of modern probability theory, and has been used in the most latest theoretical advances in addition to 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 take pleasure in 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 creator for several years in graduate courses at two of the most prestigious French universities. The truth that proofs are given with full details makes the book particularly suitable for self-study. The a lot of exercises assist the reader to get aware of the tools of stochastic calculus.

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