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Technical Multidimensional Stochastic Processes as Rough Paths: Theory and Applications

Posted on 2010-05-07




Name:Technical Multidimensional Stochastic Processes as Rough Paths: Theory and Applications
ASIN/ISBN:0521876079
Publish Date:2010
Pages:670 pages
File size:3.6 Mb
Publish Date: 2010
ISBN: 0521876079
Pages: 670 pages
File Type: PDF
File Size: 3,6 MB
Other Info: Cambridge University Press
   Technical Multidimensional Stochastic Processes as Rough Paths: Theory and Applications

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Peter K. Friz, Nicolas B. Victoir, "Multidimensional Stochastic Processes as Rough Paths: Theory and Applications"

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.

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