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.
Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space
Tubaro, Luciano;Da Prato, Giuseppe;Barbu, Viorel
2009
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.File in questo prodotto:
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euclid.aop.1248182143.pdf
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