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Stochastic differential equations driven by processes generated by divergence form operators II : convergence results
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 387-411 Cet article a éte moissonné depuis la source Numdam

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

DOI : 10.1051/ps:2007040
Classification : 60H10, 60J60
Keywords: rough paths, stochastic differential equations, stochastic process generated by divergence form operators, condition UTD, convergence of stochastic integrals 
@article{PS_2008__12__387_0,
     author = {Lejay, Antoine},
     title = {Stochastic differential equations driven by processes generated by divergence form operators {II} : convergence results},
     journal = {ESAIM: Probability and Statistics},
     pages = {387--411},
     year = {2008},
     publisher = {EDP-Sciences},
     volume = {12},
     doi = {10.1051/ps:2007040},
     mrnumber = {2437716},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007040/}
}
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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

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