An exposition of some basic features of strictly stationary, reversible Markov chains

TL;DR

This paper provides an accessible review of the fundamental properties of strictly stationary, reversible Markov chains, emphasizing their unique symmetrical features using basic measure-theoretic probability techniques.

Contribution

It offers a clear exposition of the core mathematical features of reversible Markov chains, highlighting their symmetry and foundational properties.

Findings

Reversible Markov chains exhibit special symmetry properties.

The paper clarifies the basic features of stationary, reversible Markov chains.

It uses simple measure-theoretic techniques for exposition.

Abstract

It has been well known for some time that for strictly stationary Markov chains that are ``reversible'', that special symmetry provides special extra features in the mathematical theory. This paper here is primarily a purely expository review of some of the basic features of that special theory. The mathematical techniques employed in this review are relatively gentle, involving only some basic measure-theoretic probability theory.