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, Volume 47 (2011) no. 3, p. 699-724

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.

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.

DOI : https://doi.org/10.1214/10-AIHP381
Classification:  60J60,  47D07,  15A63,  31C25
Keywords: 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},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {3},
     year = {2011},
     pages = {699-724},
     doi = {10.1214/10-AIHP381},
     zbl = {1230.60081},
     mrnumber = {2841072},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 47 (2011) no. 3, pp. 699-724. doi : 10.1214/10-AIHP381. http://www.numdam.org/item/AIHPB_2011__47_3_699_0/

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