Loading…

Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups

We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces. More precisely, we prove that for Markov-Feller semigroup in discrete time and stochasticall...

Full description

Saved in:
Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2024, Vol.40 (1), p.1-16
Main Authors: Liu, Yong, Liu, Zi-yu
Format: Article
Language:English
Subjects:
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces. More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous Markov-Feller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior, then the e-property is satis ed 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 stochastically continuous continuous-time Markov-Feller semigroups.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-023-1072-5