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Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space. II. (English. French summary) Zbl 1230.60081
The authors consider a symmetric Dirichlet form, and then define a weak solution of the Neumann problem denoted by $$\varphi$$. By considering the Kolmogorov operator associated to the Dirichlet from above, they study the existence and regularity of the solutions to the Neumann problem associated with a Ornstein-Uhlenbeck operator on a bounded and smooth convex set of a Hilbert space.
Furthermore, the authors find the solution of a stochastic variational inequality, developing the reflection problem.
For part I, cf. [Ann. Probab. 37, No. 4, 1427–1458 (2009; Zbl 1205.60141)].

##### MSC:
 60J60 Diffusion processes 47D07 Markov semigroups and applications to diffusion processes 15A63 Quadratic and bilinear forms, inner products 31C25 Dirichlet forms
Zbl 1205.60141
Full Text:
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