Displaying similar documents to “Adjoints of solution semigroups and identifiability of delay differential equations in Hilbert spaces.”

On analyticity of Ornstein-Uhlenbeck semigroups

Beniamin Goldys (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let ( R t be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let μ denote its Gaussian invariant measure. We show that the semigroup ( R t is analytic in L 2 μ 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.