Equicontinuous Families of Markov Operators in View of Asymptotic Stability

TL;DR

This paper investigates the relationship between equicontinuity, the e property, and the stability of Markov operators, establishing conditions under which asymptotic stability implies the e property.

Contribution

It demonstrates that asymptotically stable Markov operators with certain invariant measures satisfy the e property, linking stability and equicontinuity in Markov operator theory.

Findings

Asymptotic stability implies the e property under specific conditions.

Invariant measures with nonempty support interior are key to the e property.

The study clarifies the connection between stability and equicontinuity in Markov operators.

Abstract

Relation between equicontinuity, the so called e property and stability of Markov operators is studied. In particular, it is shown that any asymptotically stable Markov operator with an invariant measure such that the interior of its support is nonempty satisfies the e property.