A Course on Rough Paths

With an Introduction to Regularity Structures

  • Peter K. Friz
  • Martin Hairer

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Peter K. Friz, Martin Hairer
    Pages 1-12
  3. Peter K. Friz, Martin Hairer
    Pages 13-26
  4. Peter K. Friz, Martin Hairer
    Pages 27-46
  5. Peter K. Friz, Martin Hairer
    Pages 47-66
  6. Peter K. Friz, Martin Hairer
    Pages 67-82
  7. Peter K. Friz, Martin Hairer
    Pages 83-94
  8. Peter K. Friz, Martin Hairer
    Pages 95-103
  9. Peter K. Friz, Martin Hairer
    Pages 105-122
  10. Peter K. Friz, Martin Hairer
    Pages 123-128
  11. Peter K. Friz, Martin Hairer
    Pages 129-147
  12. Peter K. Friz, Martin Hairer
    Pages 149-168
  13. Peter K. Friz, Martin Hairer
    Pages 169-190
  14. Peter K. Friz, Martin Hairer
    Pages 191-210
  15. Peter K. Friz, Martin Hairer
    Pages 211-220
  16. Peter K. Friz, Martin Hairer
    Pages 221-240
  17. Back Matter
    Pages 241-251

About this book

Introduction

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.

Keywords

Gaussian Processes Regularity Structures Robust Stochastic Integration Rough Paths Stochastic Analysis Stochastic Differential Equations Stochastic Partial Differential Equations

Authors and affiliations

  • Peter K. Friz
    • 1
  • Martin Hairer
    • 2
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany
  2. 2.Mathematics DepartmentThe University of WarwickCoventryUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-08332-2
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-08331-5
  • Online ISBN 978-3-319-08332-2
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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