A large class of stochastic semilinear equations with measurable nonlinear term on a Hilbert space H is considered. Assuming the corresponding nonsymmetric Ornstein-Uhlenbeck process has an invariant measure μ, we prove in the spaces the existence of a transition semigroup for the equations. Sufficient conditions are provided for hyperboundedness of and for the Log Sobolev Inequality to hold; and in the case of a bounded nonlinear term, sufficient and necessary conditions are obtained. We prove the existence, uniqueness and some regularity of an invariant density for . A characterization of the domain of the generator is also given. The main tools are the Girsanov transform and Miyadera perturbations.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm396-0-1,
author = {Anna Chojnowska-Michalik},
title = {Transition semigroups for stochastic semilinear equations on Hilbert spaces},
series = {GDML\_Books},
year = {2001},
zbl = {0991.60049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm396-0-1}
}
Anna Chojnowska-Michalik. Transition semigroups for stochastic semilinear equations on Hilbert spaces. GDML_Books (2001), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm396-0-1/