Time inhomogeneous Markov chains with wave-like behavior

TL;DR

This paper introduces a novel class of time inhomogeneous Markov chains generated by iteratively transporting a base kernel via a bijection, revealing interesting behaviors and providing quantitative analysis for specific cases.

Contribution

It presents a new construction method for time inhomogeneous Markov chains using bijections, expanding understanding of their dynamics and properties.

Findings

Examples exhibit wave-like behavior.

Quantitative results characterize chain dynamics.

Construction generalizes previous models.

Abstract

Starting from a given Markov kernel on a finite set $V$ and a bijection $g$ of $V$, we construct and study a time inhomogeneous Markov chain whose kernel at time $n$ is obtained from $K$ by transport of $g^{n-1}$. We show that this construction leads to interesting examples, and we obtain quantitative results for some of these examples.