### Domain identification for analytic Ornstein-Uhlenbeck operators

van Neerven, J *(Delft University of Technology)*

Thursday 14 January 2010, 16:30-17:30

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

Let (P(t)) be the Ornstein-Uhlenbeck semigroup associated with
the stochastic Cauchy problem dU(t) = AU(t)dt + dW_H(t), where A is the
generator of a C_0-semigroup (S(t)) on a Banach space E, H is a Hilbert
subspace of E, and (W_H(t)) is an H-cylindrical Brownian motion. Assuming
that (S(t)) restricts to a C_0-semigroup on H, we obtain L^p-bounds for the
gradient D_H P(t). We show that if (P(t)) is analytic, then the invariance
assumption is fulfilled. As an application we determine the L^p-domain of
the generator of (P(t)) explicitly in the case where (S(t)) restricts to a
C_0-semigroup on H which is similar to an analytic contraction semigroup.
This is joint work with Jan Maas.

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