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.

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}, publisher = {EDP-Sciences}, volume = {12}, year = {2008}, doi = {10.1051/ps:2007040}, mrnumber = {2437716}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2007040/} }

TY - JOUR AU - Lejay, Antoine TI - Stochastic differential equations driven by processes generated by divergence form operators II : convergence results JO - ESAIM: Probability and Statistics PY - 2008 SP - 387 EP - 411 VL - 12 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2007040/ DO - 10.1051/ps:2007040 LA - en ID - PS_2008__12__387_0 ER -

%0 Journal Article %A Lejay, Antoine %T Stochastic differential equations driven by processes generated by divergence form operators II : convergence results %J ESAIM: Probability and Statistics %D 2008 %P 387-411 %V 12 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2007040/ %R 10.1051/ps:2007040 %G en %F PS_2008__12__387_0

Lejay, Antoine. Stochastic differential equations driven by processes generated by divergence form operators II : convergence results. ESAIM: Probability and Statistics, Volume 12 (2008), pp. 387-411. doi : 10.1051/ps:2007040. http://www.numdam.org/articles/10.1051/ps:2007040/

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