Differential Equations Driven by Rough Paths

École d'Été de Probabilités de Saint-Flour XXXIV - 2004

  • Terry J. Lyons
  • Michael Caruana
  • Thierry Lévy

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

Table of contents

About this book

Introduction

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

Authors and affiliations

  • Terry J. Lyons
    • 1
  • Michael Caruana
    • 1
  • Thierry Lévy
    • 2
  1. 1.Mathematical InstituteUniversity of OxfordOxford OX1 3LBUK
  2. 2.Départment de Mathématiques et ApplicationsÉcole Normale SupérieureParis Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71285-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-71284-8
  • Online ISBN 978-3-540-71285-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book