Differential Equations Driven by Rough Paths École d'Été de Probabilités de Saint-Flour XXXIV - 2004 /

• Main Authors: Lyons, Terry J. (Author), Caruana, Michael (Author), Lévy, Thierry (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Lecture Notes in Mathematics, 1908
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Differential equations.; Probabilities.; Analysis.; Probability Theory and Stochastic Processes.; Ordinary Differential Equations.
• Physical Description: XVIII, 116 p. online resource.
• ISBN: 9783540712855
• ISSN: 0075-8434 ;

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.