The theory of rough paths allows to define integrals of differential forms against irregular paths and differential equations controlled by irregular paths. This theory makes use of an extension of the notion of iterated integrals of the paths, whose algebraic properties appear to be fundamental. Stochastic processes give natural class of paths for which such integrals or differential equations are required, and this theory may be used for many types of stochastic processes.
Download the article An Introduction to Rough Paths as a postscript file (version of December, 10 2002).
This article shall appear in 2003 in the volume XXXVII of Séminaire de probabilités (Lecture Notes in Mathematics, Springer-Verlag).
This article aims to be a short presentation of the results from the article Differential equations driven by rough signals by T. Lyons and the book System Control and Rough Paths by T. Lyons and Z. Qian.
A bibliography [HTML, BiBTeX] on that subject is accessible on the site Computational Rough Paths of Djalil Chafaï (currently a post-doc at Oxford University).
Rough paths theory in one page.
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