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

Published online by Cambridge University Press:  08 September 2006

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

Keywords

Rough pathsstochastic differential equationsstochastic process generated by divergence-form operatorsDirichlet processapproximation of trajectories.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 10 , February 2006 , pp. 356 - 379
Copyright
© EDP Sciences, SMAI, 2006

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