Séminaire de Probabilités XXXVII pp 1-59

Part of the Lecture Notes in Mathematics book series (LNM, volume 1832)

An Introduction to Rough Paths

  • Antoine Lejay
Chapter

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Antoine Lejay
    • 1
  1. 1.Projet OMEGA (INRIA Lorraine)IECN, Campus scientifiqueVandœuvre-lès-Nancy CedexFrance

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