Stochastic differential equations driven by processes generated by divergence form operators II: convergence results
INRIA & Institut Élie Cartan UMR 7502,
Nancy-Université, CNRS, INRIA.
Campus scientifique, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France; Antoine.Lejay@iecn.u-nancy.fr
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.
Mathematics Subject Classification: 60H10 / 60J60
Key words: Rough paths / stochastic differential equations / stochastic process generated by divergence form operators / Condition UTD / convergence of stochastic integrals
© EDP Sciences, SMAI, 2008