On the convergence of stochastic integrals driven by processes converging on account of a homogenization property.

Lejay, Antoine

Displaying similar documents to “On the convergence of stochastic integrals driven by processes converging on account of a homogenization property.”

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

Antoine Lejay (2008)

ESAIM: Probability and Statistics

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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...

Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem

Antoine Lejay (2006)

ESAIM: Probability and Statistics

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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.