The Annals of Probability

Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space

Viorel Barbu, Giuseppe Da Prato, and Luciano Tubaro

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We consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set K with nonempty interior and regular boundary Σ in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on Σ.

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Ann. Probab., Volume 37, Number 4 (2009), 1427-1458.

First available in Project Euclid: 21 July 2009

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Primary: 60J60: Diffusion processes [See also 58J65] 47D07: Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx} 15A63: Quadratic and bilinear forms, inner products [See mainly 11Exx] 31C25: Dirichlet spaces

Reflected process convex sets Dirichlet forms Kolmogorov operators Gaussian measures infinite-dimensional Neumann problem


Barbu, Viorel; Da Prato, Giuseppe; Tubaro, Luciano. Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space. Ann. Probab. 37 (2009), no. 4, 1427--1458. doi:10.1214/08-AOP438.

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