Displaying similar documents to “Poincaré inequality for some measures in Hilbert spaces and application to spectral gap for transition semigroups”

Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces

Marco Fuhrman (1995)

Studia Mathematica

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We consider a semigroup acting on real-valued functions defined in a Hilbert space H, arising as a transition semigroup of a given stochastic process in H. We find sufficient conditions for analyticity of the semigroup in the L 2 ( μ ) space, where μ is a gaussian measure in H, intrinsically related to the process. We show that the infinitesimal generator of the semigroup is associated with a bilinear closed coercive form in L 2 ( μ ) . A closability criterion for such forms is presented. Examples are...

Uniform exponential ergodicity of stochastic dissipative systems

Beniamin Goldys, Bohdan Maslowski (2001)

Czechoslovak Mathematical Journal

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We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in ℝ d with d ≤ 3 .

The domain of the Ornstein-Uhlenbeck operator on an L p -space with invariant measure

Giorgio Metafune, Jan Prüss, Abdelaziz Rhandi, Roland Schnaubelt (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We show that the domain of the Ornstein-Uhlenbeck operator on L p ( ℝ N , μ d x ) equals the weighted Sobolev space W 2 , p ( ℝ N , μ d x ) , where μ d x is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.