Large and moderate deviations for bounded functions of slowly mixing markov chains

TL;DR

This paper establishes polynomial large and moderate deviation inequalities for bounded functions of slowly mixing Markov chains, with applications to probability and dynamical systems, demonstrating the sharpness of these inequalities.

Contribution

It introduces new polynomial deviation inequalities for polynomially mixing Markov chains, extending existing results to weaker mixing conditions.

Findings

Derived sharp polynomial large deviations inequalities

Established moderate deviations bounds for slowly mixing chains

Applied inequalities to examples in probability and dynamical systems

Abstract

We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities. These inequalities can be applied in various natural situations coming from probability theory or dynamical systems. Finally, we discuss examples from these various settings showing that our inequalities are sharp.