ESAIM: P&S, September 2006, Vol. 10, pp. 356-379
DOI: 10.1051/ps:2006015

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

Antoine Lejay

Projet OMEGA (INRIA Lorraine), IECN, Campus scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex, France; Antoine.Lejay@iecn.u-nancy.fr

(Received April 05, 2005. Revised May 12, 2006. Published online: 8 September 2006.)

Abstract
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