Stochastic differential equations driven by processes generated by divergence form operators II : convergence results
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 387-411.

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 constructed for stochastic processes generated by divergence form operators by using time-reversal techniques.

DOI : https://doi.org/10.1051/ps:2007040
Classification : 60H10,  60J60
Mots clés : rough paths, stochastic differential equations, stochastic process generated by divergence form operators, condition UTD, convergence of stochastic integrals
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title = {Stochastic differential equations driven by processes generated by divergence form operators {II} : convergence results},
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Lejay, Antoine. Stochastic differential equations driven by processes generated by divergence form operators II : convergence results. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 387-411. doi : 10.1051/ps:2007040. http://www.numdam.org/articles/10.1051/ps:2007040/

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