Innite dimensional reflecting Ornstein-Uhlenbeck stochastic process on non-convex open sets

Abstract

In this article we introduce the Gaussian Sobolev space W^1,2(O,γ ), where O is an arbitrary open set of a separable Banach space E endowed with a non-degenerate centered Gaussian measure γ. Moreover, we investigate the semi-martingale structure of the infinite dimensional reflecting Ornstein-Uhlenbeck process for open sets of the form O = {x ∈ 2 E : G(x) < 0}, where G is some Borel function on E.

Keywords: Gaussian Sobolev space; Ornstein-Uhlenbeck process; Skorohod equation; Quasi-regular Dirichlet forms