On a class of stochastic semilinear PDE's

Details On a class of stochastic semilinear PDE's On a class of stochastic semilinear PDE's

2005-09-20

arxiv.org/abs/math/0509446v1

Mathematics

Probability

28 pages

Scientific paper

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 $L^2(H;\nu)$, where $\nu$ 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 Poincar\'e inequality, a logarithmic Sobolev inequality and the ipercontractivity of the transition semigroup.

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