Infinite 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