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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