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stochastic process generated by divergence form operators

ESAIM: Probability and Statistics (1)

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

ESAIM: Probability and Statistics / Volume 12 / 2008

Published online by Cambridge University Press:

25 July 2008, pp. 387-411

Print publication:

2008
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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.