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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)].

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: DOI EuDML
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