Yet another introduction to rough paths

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1979)

Abstract

This specialized course provides another point of view on the theory of rough paths, starting with simple considerations on ordinary integrals, and stressing the importance of the Green-Riemann formula, as in the work of D. Feyel and A. de La Pradelle. This point of view allows us to gently introduce the required algebraic structures and provides alternative ways to understand why the construction of T. Lyons et al. is a natural generalization of the notion of integral of differential forms, in the sense that it shares the same properties as integrals along smooth paths, when we use the “right notion” of a path.

Key words

Rough paths integral of differential forms along irregular paths controlled differential equations Lie algebra Lie group Chen series sub ‐ Riemannian geometry 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Èquipe-Projet TOSCAInstitut Èlie Cartan (Nancy-Universitè, CNRS, INRIA) Campus scientifiqueVandoeuvre-lès-NancyFrance

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