Multidimensional Stochastic Processes as Rough Paths (Cambridge Studies in Advanced Mathematics #120) (Hardcover)

Multidimensional Stochastic Processes as Rough Paths (Cambridge Studies in Advanced Mathematics #120) By Peter K. Friz, Nicolas B. Victoir Cover Image

Multidimensional Stochastic Processes as Rough Paths (Cambridge Studies in Advanced Mathematics #120) (Hardcover)

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Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.
Product Details ISBN: 9780521876070
ISBN-10: 0521876079
Publisher: Cambridge University Press
Publication Date: March 15th, 2010
Pages: 670
Language: English
Series: Cambridge Studies in Advanced Mathematics