Stochastic differential equations driven by processes generated by divergence form operators II : convergence results

Lejay, Antoine

ESAIM: Probability and Statistics, Tome 12 (2008), pp. 387-411.

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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