Transition semigroups for stochastic semilinear equations on Hilbert spaces

Anna Chojnowska-Michalik. Transition semigroups for stochastic semilinear equations on Hilbert spaces. 2001. <http://eudml.org/doc/285990>.

@book{AnnaChojnowska2001,
abstract = {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 $L^\{p\}(H,μ)$ spaces the existence of a transition semigroup $(P_\{t\})$ for the equations. Sufficient conditions are provided for hyperboundedness of $P_\{t\}$ 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 $(P_\{t\})$. A characterization of the domain of the generator is also given. The main tools are the Girsanov transform and Miyadera perturbations.},
author = {Anna Chojnowska-Michalik},
keywords = {transition semigroups; stochastic semilinear equations; Girsanov transform; hyperboundedness; log Sobolev inequality; invariant measure; density},
language = {eng},
title = {Transition semigroups for stochastic semilinear equations on Hilbert spaces},
url = {http://eudml.org/doc/285990},
year = {2001},
}

TY - BOOK
AU - Anna Chojnowska-Michalik
TI - Transition semigroups for stochastic semilinear equations on Hilbert spaces
PY - 2001
AB - 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 $L^{p}(H,μ)$ spaces the existence of a transition semigroup $(P_{t})$ for the equations. Sufficient conditions are provided for hyperboundedness of $P_{t}$ 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 $(P_{t})$. A characterization of the domain of the generator is also given. The main tools are the Girsanov transform and Miyadera perturbations.
LA - eng
KW - transition semigroups; stochastic semilinear equations; Girsanov transform; hyperboundedness; log Sobolev inequality; invariant measure; density
UR - http://eudml.org/doc/285990
ER -