Yet another introduction to rough paths

Antoine Lejay 1, 2
2 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : This article provides another point of view on the theory of rough paths, which starts with simple considerations on ordinary integrals, and endows theimportance of the Green-Riemann formula, as in the work of D. Feyel and A. de La Pradelle. This point of view allows us to introduce gently the required algebraic structures and provides alternative ways to understand why the construction provided by T. Lyons et al. is a natural generalization of the notion of integral of differential forms, in the sense it shares the same properties as integrals along smooth paths, when we use the ``right notion'' of path.
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Antoine Lejay. Yet another introduction to rough paths. Séminaire de Probabilités, Springer-Verlag, 2009, Séminaire de Probabilités XLII / Lecture Notes in Mathematics, 1979, pp.1-101. ⟨10.1007/978-3-642-01763-6_1⟩. ⟨inria-00107460v3⟩

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