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.

Author: Peter K. Friz, Nicolas B. Victoir
Binding Type: Hardcover
Publisher: Cambridge University Press
Published: 03/15/2010
Series: Cambridge Studies in Advanced Mathematics #120
Pages: 670
Weight: 2.2lbs
Size: 9.00h x 6.10w x 1.50d
ISBN: 9780521876070

About the Author
Friz, Peter K.: - Peter K. Friz is a Reader in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. He is also a Research Group Leader at the Johann Radon Institute at the Austrian Academy of Sciences, Linz.Victoir, Nicolas B.: - Nicolas B. Victoir works in quantitative research at JPMorgan in Hong Kong.