Date: 12 Dec 2003

An Introduction to Rough Paths

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Abstract

This article aims to be an introduction to the theory of rough paths, in which integrals of differential forms against irregular paths and differential equations controlled by irregular paths are defined. This theory makes use of an extension of the notion of iterated integrals of the paths, whose algebraic properties appear to be fundamental. This theory is well-suited for stochastic processes.

Keywords: controlled differential equations, integration against irregular paths, p-variation, stochastic processes, iterated integrals, Chen series, geometric multiplicative functional