A Course on Rough Paths: With an Introduction to Regularity Structures by Peter K. FrizA Course on Rough Paths: With an Introduction to Regularity Structures by Peter K. Friz

A Course on Rough Paths: With an Introduction to Regularity Structures

byPeter K. Friz, Martin Hairer

Paperback | September 4, 2014

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Lyons' rough path analysis has provided new insights in the analysis of stochastic differential equations and stochastic partial differential equations, such as the KPZ equation. This textbook presents the first thorough and easily accessible introduction to rough path analysis.

When applied to stochastic systems, rough path analysis provides a means to construct a pathwise solution theory which, in many respects, behaves much like the theory of deterministic differential equations and provides a clean break between analytical and probabilistic arguments. It provides a toolbox allowing to recover many classical results without using specific probabilistic properties such as predictability or the martingale property. The study of stochastic PDEs has recently led to a significant extension - the theory of regularity structures - and the last parts of this book are devoted to a gentle introduction.

Most of this course is written as an essentially self-contained textbook, with an emphasis on ideas and short arguments, rather than pushing for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis courses and has some interest in stochastic analysis. For a large part of the text, little more than Itô integration against Brownian motion is required as background.

Peter K. Friz is presently a full professor at TU and WIAS Berlin, previous professional affiliations include Cambridge University, Merrill Lynch. He holds a PhD from the Courant Institute of New York University. PKF has made contributions to the understanding of the Navier-Stokes equation as dynamical system, pioneered new asymptotic ...
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Title:A Course on Rough Paths: With an Introduction to Regularity StructuresFormat:PaperbackDimensions:251 pagesPublished:September 4, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319083317

ISBN - 13:9783319083315

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Table of Contents

Introduction.- The space of rough paths.- Brownian motion as a rough path.- Integration against rough paths.- Stochastic integration and ItËo's formula.- Doob-Meyer type decomposition for rough paths.- Operations on controlled rough paths.- Solutions to rough differential equations.- Stochastic differential equations.- Gaussian rough paths.- Cameron-Martin regularity and applications.- Stochastic partial differential equations.- Introduction to regularity structures.- Operations on modelled distributions.- Application to the KPZ equation.

Editorial Reviews

"The book under review is a concise introduction tothe theory of rough paths, their applications in stochastic analysis, and torecent extensions allowing to handle stochastic partial differential equations.. It is easy to base a graduate course on rough paths on this monograph. . aresearcher who carefully works her way through all of the exercises will have avery good impression of the current state of the art in rough paths . ." (NicolasPerkowski, zbMATH 1327.60013, 2016)