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

Abstract

We have seen in a previous article how the theory of 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 Ito integrals already constructed for stochastic processes generated by divergence form operators by using time-reversal techniques.