Geodesic
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

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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.

DOI : 10.1051/ps:2006015
Classification : 60H10, 60J60
Keywords: rough paths, stochastic differential equations, stochastic process generated by divergence-form operators, Dirichlet process, approximation of trajectories 
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     author = {Lejay, Antoine},
     title = {Stochastic differential equations driven by processes generated by divergence form operators {I} : a {Wong-Zakai} theorem},
     journal = {ESAIM: Probability and Statistics},
     pages = {356--379},
     publisher = {EDP-Sciences},
     volume = {10},
     year = {2006},
     doi = {10.1051/ps:2006015},
     mrnumber = {2247926},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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

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