Subgaussian concentration inequalities for geometrically ergodic Markov chains

TL;DR

This paper establishes a precise equivalence between geometric ergodicity of Markov chains and subgaussian deviation inequalities for bounded functionals, providing a new characterization of ergodic behavior.

Contribution

It proves that geometric ergodicity of Markov chains is equivalent to subgaussian concentration inequalities for bounded functionals, offering a novel theoretical insight.

Findings

Geometric ergodicity implies subgaussian deviation inequalities.

Subgaussian inequalities characterize geometric ergodicity.

Provides a new criterion for ergodic Markov chains.

Abstract

We prove that an irreducible aperiodic Markov chain is geometrically ergodic if and only if any separately bounded functional of the stationary chain satisfies an appropriate subgaussian deviation inequality from its mean.