Stability of transition semigroups and applications to parabolic equations
Abstract
The paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochastic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.
Keywords
Cite
@article{arxiv.2005.01430,
title = {Stability of transition semigroups and applications to parabolic equations},
author = {Moritz Gerlach and Jochen Glück and Markus Kunze},
journal= {arXiv preprint arXiv:2005.01430},
year = {2021}
}
Comments
25 pages. This article originally emerged from a subsection of arXiv:1705.01587v1 that was split into a separate paper. The final results in the present paper are, however, stronger and more general than those from the removed subsection of arXiv:1705.01587v1. This is version 4; various changes in the presentation compared to v3