# Asymptotic stability for non-equicontinuous Markov semigroups

## TL;DR

This paper introduces a new criterion for the asymptotic stability of non-equicontinuous Markov semigroups, including an example with essential randomness demonstrating stability.

## Contribution

It formulates a novel stability criterion for eventually continuous semigroups and provides an explicit example with essential randomness.

## Key findings

- Established a new criterion for asymptotic stability.
- Provided an example of a non-equicontinuous semigroup with essential randomness.
- Demonstrated stability under the new criterion.

## Abstract

We formulate a new criterion of the asymptotic stability for some non-equicontinuous Markov semigroups, the so-called eventually continuous semigroups. In particular, we provide a non-equicontinuous Markov semigroup example with essential randomness, which is asymptotically stable.