Infinite dimensional reflecting Ornstein-Uhlenbeck stochastic process

2015/01/06 by Akhlil, Khalid
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1501.01248

Abstract

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∈ E : G(x)<0\, where G is some Borel function on E.

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