A fourth moment inequality for functionals of stationary processes

TL;DR

This paper establishes a fourth moment inequality for partial sums of functionals of strongly ergodic Markov chains, aiding the study of empirical process invariance principles and applicable to certain dynamical systems.

Contribution

It introduces a new fourth moment bound tailored for strongly ergodic Markov chains and dynamical systems with specific spectral properties, enhancing existing analytical tools.

Findings

Provides a new fourth moment inequality for Markov chains

Extends the inequality to certain dynamical systems

Includes applications demonstrating practical relevance

Abstract

In this paper, a fourth moment bound for partial sums of functional of strongly ergodic Markov chain is established. This type of inequality plays an important role in the study of empirical process invariance principle. This one is specially adapted to the technique of Dehling, Durieu and Voln\'y (2008). The same moment bound can be proved for dynamical system whose transfer operator has some spectral properties. Examples of applications are given.