Multidimensional Stochastic Processes as Rough Paths : Theory and Applications - Peter K. Friz

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Multidimensional Stochastic Processes as Rough Paths

Theory and Applications

By: Peter K. Friz, Nicolas B. Victoir

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Hardcover | 4 February 2010

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672 Pages

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22.86 x 15.24 x 3.66

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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.

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Preface
Introduction
The story in a nutshell
Basics
Continuous paths of bounded variation
Riemann-Stieltjes integration
Ordinary differential equations (ODEs)
ODEs: smoothness
Variation and H¶lder spaces
Young integration
Abstract Theory of Rough Paths
Free nilpotent groups
Variation and H¶lder spaces on free groups
Geometric rough path spaces
Rough differential equations (RDEs)
RDEs: smoothness
RDEs with drift and other topics
Stochastic Processes Lifted to Rough Paths
Brownian motion
Continuous (semi)martingales
Gaussian processes
Markov processes
Applications to Stochastic Analysis
Stochastic differential equations and stochastic flows
Stochastic Taylor expansions
Support theorem and large deviations
Malliavin calculus for RDEs
Appendix: A. Sample path regularity and related topics
Banach calculus
Large deviations
Gaussian analysis
Analysis on local Dirichlet spaces
Frequently used notation
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Multidimensional Stochastic Processes as Rough Paths

Theory and Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

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