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Stochastic differential equations driven by processes generated by divergence form operators II: convergence results

Published online by Cambridge University Press:  25 July 2008

Antoine Lejay
Antoine Lejay*
Affiliation:
Projet TOSCA, INRIA & Institut Élie Cartan UMR 7502, Nancy-Université, CNRS, INRIA. Campus scientifique, BP 239, 54506 Vandœuvre-lès-Nancy Cedex, France; Antoine.Lejay@iecn.u-nancy.fr
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Abstract

We have seen in a previous article how the theory of “rough paths”allows us to construct solutions of differential equations driven by processes generated by divergence form operators. In this article, we study a convergence criterion which implies that one can interchange the integral with the limit of a family of stochastic processes generated by divergence form operators. As a corollary, we identify stochastic integrals constructed with the theory of rough paths with Stratonovich or Itô integrals already constructedfor stochastic processes generated by divergence form operators by using time-reversal techniques.

Keywords

Rough pathsstochastic differential equationsstochastic process generated by divergence form operatorsCondition UTDconvergence of stochastic integrals

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 387 - 411
Copyright
© EDP Sciences, SMAI, 2008

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