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.

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.

DOI : 10.1214/10-AIHP381
Classification : 60J60, 47D07, 15A63, 31C25
Mots-clés : Neumann problem, Ornstein-Uhlenbeck operator, Kolmogorov operator, reflection problem, infinite-dimensional analysis 
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     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},
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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://archive.numdam.org/articles/10.1214/10-AIHP381/

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