On regularity of functions of Markov chains

TL;DR

This paper introduces new sufficient conditions under which functions of finite-state Markov chains exhibit regularity, meaning past values have diminishing influence on current distributions, despite not being Markov themselves.

Contribution

The paper provides novel criteria for the regularity of functions of finite-state Markov chains, expanding understanding of their long-term dependence properties.

Findings

Established new sufficient conditions for regularity.

Demonstrated that functions of Markov chains can be regular without being Markov.

Enhanced theoretical understanding of dependence decay in Markov-derived processes.

Abstract

We consider processes which are functions of finite-state Markov chains. It is well known that such processes are rarely Markov. However, such processes are often regular in the following sense: the distant past values of the process have diminishing influence on the distribution of the present value. In the present paper, we present novel sufficient conditions for regularity of functions of Markov chains.