Brownian Motion, Martingales, and Stochastic Calculus (Hardcover, 1st ed. 2016)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Graduate Texts in Mathematics, 274
Release date:	May 2016
First published:	2016
Authors:	Jean-Francois Le Gall
Dimensions:	242 x 160 x 22mm (L x W x T)
Format:	Hardcover
Pages:	273
Edition:	1st ed. 2016
ISBN-13:	978-3-319-31088-6
Languages:	English
Subtitles:	French
Categories:	Books > Business & Economics > Finance & accounting > General Books > Science & Mathematics > Mathematics > Probability & statistics Books > Reference & Interdisciplinary > Communication studies > Information theory > Cybernetics & systems theory Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling
LSN:	3-319-31088-7
Barcode:	9783319310886

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