Brownian Motion, Martingales, and Stochastic Calculus

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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

 

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Author : Jean-François Le Gall

Pages : 273 pages

Publisher : Springer

Language :

ISBN-10 : 3319310887

ISBN-13 : 9783319310886

 

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Brownian Motion, Martingales, and Stochastic Calculus

 

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