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Semi-martingales and rough paths theory

Laure Coutin 1 Antoine Lejay 2, 3
2 OMEGA - Probabilistic numerical methods
CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We prove that the theory of rough paths, which is used to define path-wise integrals and path-wise differential equations, can be used with continuous semi-martingales. We provide then an almost sure theorem of type Wong-Zakai. Moreover, we show that the conditions UT and UCV, used to prove that one can interchange limits and Ito or Stratonovich integrals, provide the same result when one uses the rough paths theory.
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Contributor : Antoine Lejay <>
Submitted on : Sunday, September 10, 2006 - 12:03:41 PM
Last modification on : Thursday, February 25, 2021 - 10:54:05 AM
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  • HAL Id : inria-00000411, version 1


Laure Coutin, Antoine Lejay. Semi-martingales and rough paths theory. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2005, 10 (23), pp.761-785. ⟨inria-00000411⟩



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