Hoeffding's inequality for non-irreducible Markov models

TL;DR

This paper extends Hoeffding's inequality to bounded Lipschitz functions of certain non-irreducible Markov models, using uniform ergodicity in Wasserstein space, broadening the scope of probabilistic bounds.

Contribution

It introduces Hoeffding's inequality for non-irreducible Markov models under uniform ergodicity assumptions, filling a gap in existing probabilistic inequalities.

Findings

Hoeffding's inequality established for non-irreducible Markov models.

Results applicable to bounded Lipschitz functions.

Broadens understanding of concentration inequalities in Markov processes.

Abstract

In this article, we establish Hoeffding's inequality for bounded Lipschitz functions of a class of not necessarily irreducible Markov models. The result complements the existing literature on this topic where Hoeffding's inequality for bounded measurable functions of a class of irreducible Markov models has been considered. Our approach is based on the assumption of uniform ergodicity of the underlying Markov model in $L^1$-Wasserstein space.