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

Lejay, Antoine

ESAIM: Probability and Statistics, Tome 10 (2006), pp. 356-379.

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.

Classification : 60H10, 60J60
Mots clés : rough paths, stochastic differential equations, stochastic process generated by divergence-form operators, Dirichlet process, approximation of trajectories

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