Relation between the eventual continuity and the e-property for Markov-Feller semigroups

2023/02/17 by Yong Liu, Ziyu Liu, Liu, Yong +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Banach Space Theory #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2302.08755

openalex publication_date 2023/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Asymptotic stability and mean ergodicity of Feller processes on Polish spaces
• Weak irreducibility of stochastic delay differential equation driven by pure jump noise

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