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

DOI : https://doi.org/10.1051/ps:2006015
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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     title = {Stochastic differential equations driven by processes generated by divergence form operators {I} : a {Wong-Zakai} theorem},
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     url = {http://archive.numdam.org/articles/10.1051/ps:2006015/}
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Lejay, Antoine. Stochastic differential equations driven by processes generated by divergence form operators I : a Wong-Zakai theorem. ESAIM: Probability and Statistics, Tome 10 (2006), pp. 356-379. doi : 10.1051/ps:2006015. http://archive.numdam.org/articles/10.1051/ps:2006015/

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