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  3. Multidimensional Stochastic Processes as Rough Paths
  • Cited by 387
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2010
Online ISBN:
9780511845079
DOI:
https://doi.org/10.1017/CBO9780511845079
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Probability Theory and Stochastic Processes, Statistics and Probability
Series:
Cambridge Studies in Advanced Mathematics (120)
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Book description

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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