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Title
A course on rough paths : with an introduction to regularity structures / Peter K. Friz, Martin Hairer.
ISBN
9783319083322 (electronic book)
3319083325 (electronic book)
9783319083315
Published
Cham : Springer, 2014.
Language
English
Description
1 online resource (xiv, 251 pages) : illustrations.
Item Number
10.1007/978-3-319-08332-2 doi
Call Number
QA274.23
Dewey Decimal Classification
519.2
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed September 12, 2014).
Series
Universitext.
Available in Other Form
Print version: 9783319083315
Introduction
The space of rough paths
Brownian motion as a rough path
Integration against rough paths
Stochastic integration and Itô'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.
