Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn–Hilliard equation
Giuseppe Da Prato, Arnaud Debussche, Luciano Tubaro (2004)
Annales de l'I.H.P. Probabilités et statistiques
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Displaying similar documents to “Poincaré inequality for some measures in Hilbert spaces and application to spectral gap for transition semigroups”
Irregular semi-convex gradient systems perturbed by noise and application to the stochastic Cahn–Hilliard equation
Analyticity of transition semigroups and closability of bilinear forms in Hilbert spaces
Marco Fuhrman (1995)
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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 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 . A closability criterion for such forms is presented. Examples are...
The hypercontractivity of Ornstein-Uhlenbeck semigroups with drift, revisited
Sheng-Wu He, Jia-Gang Wang (1997)
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Zhongmin Qian, Sheng-Wu He (1995)
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Invariant measures for stochastic Cauchy problems with asymptotically unstable drift semigroup.
van Gaans, Onno, van Neerven, Jan (2006)
Electronic Communications in Probability [electronic only]
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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 with .
The domain of the Ornstein-Uhlenbeck operator on an -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 equals the weighted Sobolev space , where is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.