Infinite dimensional reflecting Ornstein-Uhlenbeck stochastic process

الأصل · EN

In this article we introduce the Gaussian Sobolev space W¹,²(O,γ), where 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 O={x∈ E: G(x)<0}, where G is some Borel function on E.