inria-00107460, version 3
Yet another introduction to rough paths
Antoine Lejay
a, 1, 2
Séminaire de Probabilités 1979 (2009) 1-101
Résumé : 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.
- a – INRIA
- 1 : Institut Elie Cartan Nancy (IECN)
- CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
- 2 : TOSCA (INRIA Sophia Antipolis / INRIA Lorraine / IECN)
- INRIA – CNRS : UMR7502 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
- Domaine : Mathématiques/Analyse classique
Mathématiques/Optimisation et contrôleMathématiques/Probabilités - Mots-clés : Rough paths – integral of differential forms along irregular paths – controlled differential equations – Lie algebra – Lie group – Chen series – sub-Riemannian geometry
- Versions disponibles : v1 (18-10-2006) v2 (14-11-2007) v3 (11-12-2008)
- inria-00107460, version 3
- http://hal.inria.fr/inria-00107460
- oai:hal.inria.fr:inria-00107460
- Contributeur : Antoine Lejay
- Soumis le : Jeudi 11 Décembre 2008, 05:04:30
- Dernière modification le : Jeudi 15 Octobre 2009, 22:36:18
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