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Infinite dimensional reflecting Ornstein-Uhlenbeck stochastic process
Khalid Akhlil · 2015-01-07 · via math.PR updates on arXiv.org

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

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