Relation between the eventual continuity and the e-property for Markov-Feller semigroups
Probability
2023-02-20 v1
Abstract
We investigate the relation between the e-property and the eventual continuity, or called the asymptotic equicontinuity, which is a generalization of the e-property. We prove that, for any discrete-time or strongly continuous continuous-time eventually continuous Markov-Feller semigroup with an ergodic measure, if the interior of the support of the ergodic measure is nonempty, then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the strongly continuous continuous-time Markov-Feller semigroups.
Keywords
Cite
@article{arxiv.2302.08755,
title = {Relation between the eventual continuity and the e-property for Markov-Feller semigroups},
author = {Yong Liu and Ziyu Liu},
journal= {arXiv preprint arXiv:2302.08755},
year = {2023}
}