Stochastic Differential Equations Driven by Processes Generated by Divergence Form Operators II: Convergence results

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 : We have seen in a previous article how the theory of "rough paths" allows us to construct solutions of differential equations driven by processes generated by divergence form operators. In this article, we study a convergence criterion which implies that one can interchange the integral with the limit of a family of stochastic processes generated by divergence form operators. As a corollary, we identify stochastic integrals constructed with the theory of rough paths with Stratonovich or Itô integrals already constructed for stochastic processes generated by divergence form operators by using time-reversal techniques.
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Antoine Lejay. Stochastic Differential Equations Driven by Processes Generated by Divergence Form Operators II: Convergence results. ESAIM: Probability and Statistics, EDP Sciences, 2008, 12, pp.387-411. ⟨10.1051/ps:2007040⟩. ⟨inria-00092427v3⟩

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