On analyticity of Ornstein-Uhlenbeck semigroups
Summary: Let \((R_t)\) be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let \(\mu\) denote its Gaussian invariant measure. We show that the semigroup \((R_t)\) is analytic in \(L^2(\mu)\) if and only if its generator is variational. In particular, we show that the transition semigroup of a finite-dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.
scientific article; zbMATH DE number 1822108