Stochastic Differential Equations Driven by Processes Generated by Divergence Form Operators I: A Wong-Zakai Theorem

Antoine Lejay 1, 2
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 show in this article how the theory of "rough paths" allows us to construct solutions of differential equations (SDEs) driven by processes generated by divergence-form operators. For that, we use approximations of the trajectories of the stochastic process by piecewise smooth paths. A result of type Wong-Zakai follows immediately.
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Submitted on : Sunday, September 10, 2006 - 1:27:49 PM
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Antoine Lejay. Stochastic Differential Equations Driven by Processes Generated by Divergence Form Operators I: A Wong-Zakai Theorem. ESAIM: Probability and Statistics, EDP Sciences, 2006, 10, pp.356-379. ⟨10.1051/ps:2006015⟩. ⟨inria-00092426⟩

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