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.
Mots clés : rough paths, stochastic differential equations, stochastic process generated by divergence-form operators, Dirichlet process, approximation of trajectories
@article{PS_2006__10__356_0, author = {Lejay, Antoine}, title = {Stochastic differential equations driven by processes generated by divergence form operators {I} : a {Wong-Zakai} theorem}, journal = {ESAIM: Probability and Statistics}, pages = {356--379}, publisher = {EDP-Sciences}, volume = {10}, year = {2006}, doi = {10.1051/ps:2006015}, mrnumber = {2247926}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2006015/} }
TY - JOUR AU - Lejay, Antoine TI - Stochastic differential equations driven by processes generated by divergence form operators I : a Wong-Zakai theorem JO - ESAIM: Probability and Statistics PY - 2006 SP - 356 EP - 379 VL - 10 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2006015/ DO - 10.1051/ps:2006015 LA - en ID - PS_2006__10__356_0 ER -
%0 Journal Article %A Lejay, Antoine %T Stochastic differential equations driven by processes generated by divergence form operators I : a Wong-Zakai theorem %J ESAIM: Probability and Statistics %D 2006 %P 356-379 %V 10 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2006015/ %R 10.1051/ps:2006015 %G en %F PS_2006__10__356_0
Lejay, Antoine. Stochastic differential equations driven by processes generated by divergence form operators I : a Wong-Zakai theorem. ESAIM: Probability and Statistics, Tome 10 (2006), pp. 356-379. doi : 10.1051/ps:2006015. http://www.numdam.org/articles/10.1051/ps:2006015/
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