Séminaire de Probabilités XXXVII

Volume 1832 of the series Lecture Notes in Mathematics pp 1-59


An Introduction to Rough Paths

  • Antoine LejayAffiliated withProjet OMEGA (INRIA Lorraine), IECN, Campus scientifique

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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