Infinite dimensional reflecting Ornstein-Uhlenbeck stochastic process

Abstract

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

arXiv admin note: text overlap with arXiv:1302.2204 by other authors