Residualities and uniform ergodicities of Markov semigroups

TL;DR

This paper investigates the residual properties and uniform ergodic behaviors of Markov semigroups on abstract state spaces, utilizing a generalized Dobrushin coefficient to understand their convergence characteristics.

Contribution

It introduces a generalized Dobrushin ergodicity coefficient to analyze residualities and explores uniform mean ergodicities of Markov semigroups.

Findings

Characterization of residual sets of uniform P-ergodic Markov semigroups

Extension of ergodicity analysis using a generalized Dobrushin coefficient

Insights into uniform mean ergodicities of Markov semigroups

Abstract

The first goal of the present paper is to study residualities of the set of uniform $P$-ergodic Markov semigroups defined on abstract state spaces by means of a generalized Dobrushin ergodicity coefficient. In the last part of the paper, we explore uniform mean ergodicities of Markov semigroups.