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Title
A course on rough paths : with an introduction to regularity structures / Peter K. Friz, Martin Hairer.
Edition
Second edition.
ISBN
9783030415563 (electronic book)
3030415562 (electronic book)
3030415554
9783030415556
Published
Cham, Switzerland : Springer, [2020]
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-030-41
Call Number
QA274.23 .F75 2020
Dewey Decimal Classification
519.2
Summary
With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on online resource; title from digital title page (viewed on June 15, 2020).
Series
Universitext.
Available in Other Form
Print version: 9783030415556
1 Introduction
2 The space of rough paths
3 Brownian motion as a rough path
4 Integration against rough paths
5 Stochastic integration and Itôs formula
6 Doob-Meyer type decomposition for rough paths
7 Operations on controlled rough paths
8 Solutions to rough differential equations
9 Stochastic differential equations
10 Gaussian rough paths
11 Cameron-Martin regularity and applications
12 Stochastic partial differential equations
13 Introduction to regularity structures
14 Operations on modelled distributions
15 Application to the KPZ equation
References
Index.
