Differential Equations Driven by Rough Paths: École d’Été de Probabilités de Saint-Flour XXXIV – 2004

Terry J. Lyons, Michael Caruana, Thierry Lévy (auth.)3540712844, 9783540712848

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.

Table of contents :
Front Matter….Pages I-XVIII
Differential Equations Driven by Moderately Irregular Signals….Pages 1-24
The Signature of a Path….Pages 25-40
Rough Paths….Pages 41-61
Integration Along Rough Paths….Pages 63-79
Differential Equations Driven by Rough Paths….Pages 81-93
Back Matter….Pages 95-115