On a Class of Stochastic Semilinear PDEs |
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Authors: | Luigi Manca |
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Institution: | 1. Scuola Normale Superiore , Scuola Normale Superiore di Pisa , Pisa, Italy l.manca@sns.it |
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Abstract: | Abstract We consider stochastic semilinear partial differential equations with Lipschitz nonlinear terms. We prove existence and uniqueness of an invariant measure and the existence of a solution for the corresponding Kolmogorov equation in the space L 2(H;ν), where ν is the invariant measure. We also prove the closability of the derivative operator and an integration by parts formula. Finally, under boundness conditions on the nonlinear term, we prove a Poincaré inequality, a logarithmic Sobolev inequality, and the ipercontractivity of the transition semigroup. |
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Keywords: | Differential stochastic equation Invariant measure Kolmogorov equation Log-Sobolev inequality Spectral gap |
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