On the relationship between the reversibility of dynamics and balance conditions

W. A. Majewski

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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.