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approximation of trajectories.

ESAIM: Probability and Statistics (1)

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

ESAIM: Probability and Statistics / Volume 10 / February 2006

Published online by Cambridge University Press:

08 September 2006, pp. 356-379

Print publication:

February 2006
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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.