Dans cet article nous étudions l'existence et la régularité des solutions d'un problème de Neumann associé à un opérateur de Ornstein-Uhlenbeck défini sur un domaine convexe K, borné et régulier dans un espace de Hilbert H. Le problème est lié à un problème de réflexion associé à une équation différentielle stochastique dans le domaine K.
This work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein-Uhlenbeck operator on a bounded and smooth convex set K of a Hilbert space H. This problem is related to the reflection problem associated with a stochastic differential equation in K.
Mots clés : Neumann problem, Ornstein-Uhlenbeck operator, Kolmogorov operator, reflection problem, infinite-dimensional analysis
@article{AIHPB_2011__47_3_699_0, author = {Barbu, Viorel and Da Prato, Giuseppe and Tubaro, Luciano}, title = {Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a {Hilbert} space {II}}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {699--724}, publisher = {Gauthier-Villars}, volume = {47}, number = {3}, year = {2011}, doi = {10.1214/10-AIHP381}, mrnumber = {2841072}, zbl = {1230.60081}, language = {en}, url = {http://www.numdam.org/articles/10.1214/10-AIHP381/} }
TY - JOUR AU - Barbu, Viorel AU - Da Prato, Giuseppe AU - Tubaro, Luciano TI - Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2011 SP - 699 EP - 724 VL - 47 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/10-AIHP381/ DO - 10.1214/10-AIHP381 LA - en ID - AIHPB_2011__47_3_699_0 ER -
%0 Journal Article %A Barbu, Viorel %A Da Prato, Giuseppe %A Tubaro, Luciano %T Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II %J Annales de l'I.H.P. Probabilités et statistiques %D 2011 %P 699-724 %V 47 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/10-AIHP381/ %R 10.1214/10-AIHP381 %G en %F AIHPB_2011__47_3_699_0
Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano. Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 3, pp. 699-724. doi : 10.1214/10-AIHP381. http://www.numdam.org/articles/10.1214/10-AIHP381/
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