Volume 10, September 2006
|Page(s)||356 - 379|
|Published online||08 September 2006|
Stochastic differential equations driven by processes generated by divergence form operators I: a Wong-Zakai theorem
Projet OMEGA (INRIA Lorraine),
IECN, Campus scientifique,
54506 Vandœuvre-lès-Nancy Cedex, France; Antoine.Lejay@iecn.u-nancy.fr
Revised: 12 May 2006
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.
Mathematics Subject Classification: 60H10 / 60J60
Key words: Rough paths / stochastic differential equations / stochastic process generated by divergence-form operators / Dirichlet process / approximation of trajectories.
© EDP Sciences, SMAI, 2006
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