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  • © 2007

Differential Equations Driven by Rough Paths

Ecole d’Eté de Probabilités de Saint-Flour XXXIV-2004

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1908)

Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-XVIII
  2. Rough Paths

    Pages 41-61
  3. Back Matter

    Pages 95-115

About this book

Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory.

The goal of these notes, representing a course given by Terry Lyons in 2004, is to provide a straightforward and self supporting but minimalist account of the key results forming the foundation of the theory of rough paths. The proofs are similar to those in the existing literature, but have been refined with the benefit of hindsight. The theory of rough paths aims to create the appropriate mathematical framework for expressing the relationships between evolving systems, by extending classical calculus to the natural models for noisy evolving systems, which are often far from differentiable.

Keywords

  • Boundary value problem
  • Chen Iterated Integral
  • Coupled Systems
  • Log Signature
  • Probability theory
  • Rough Differential Equation
  • Stochastic Analysis
  • ordinary differential equations

Reviews

From the reviews:

"The present book is based on lectures delivered by Lyons at the Saint-Flour Summer School in July 2004. … It is primarily intended for a reader who has never been exposed to the theory of rough paths … . There is no doubt that the book will be useful to anyone trying to enter the sophisticated ground of rough path theory–students as well as experienced researchers." (Bohdan Maslowski, Mathematical Reviews, Issue 2009 c)

“The book provides an introduction to and a survey of the key concepts and results of the theory of rough paths. It grew out of the lecture notes for the corresponding lectures given at the Ecole d’Eté de Probabilités de Saint-Flour XXXIV – 2004. … The book is very well readable and will be useful for everyone interested in learning about the theory of rough paths.” (Evelyn Buckwar, Zentralblatt MATH, Vol. 1176, 2010)

Authors and Affiliations

  • Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK

    Terry J. Lyons, Michael Caruana

  • Départment de Mathématiques et Applications, École Normale Supérieure, Paris Cedex 05, France

    Thierry Lévy

Bibliographic Information

  • Book Title: Differential Equations Driven by Rough Paths

  • Book Subtitle: Ecole d’Eté de Probabilités de Saint-Flour XXXIV-2004

  • Authors: Terry J. Lyons, Michael Caruana, Thierry Lévy

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-71285-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2007

  • Softcover ISBN: 978-3-540-71284-8

  • eBook ISBN: 978-3-540-71285-5

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVIII, 116

  • Topics: Analysis, Probability Theory, Differential Equations

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-71285-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 49.99
Price excludes VAT (USA)