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Domain identification for analytic Ornstein-Uhlenbeck operators

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Stochastic Partial Differential Equations

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 Lp-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 Lp-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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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