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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 21 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1248182143

Digital Object Identifier
doi:10.1214/08-AOP438

Mathematical Reviews number (MathSciNet)
MR2546750

Zentralblatt MATH identifier
1205.60141

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.aop/1248182143


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