2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94703We 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.28 pagesProbability37L40; 35R60; 35K57text