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A Fourth Moment Inequality for Functionals of Stationary Processes

Part of: Measure-theoretic ergodic theory Limit theorems Markov processes Stochastic processes Nonparametric inference

Published online by Cambridge University Press:  14 July 2016

Olivier Durieu
Olivier Durieu*
Affiliation:
Université de Rouen
*
∗Postal address: Laboratoire de Mathématique Raphaël Salem, UMR 6085 CNRS, Université de Rouen, France. Email address: olivier.durieu@etu.univ-rouen.fr
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Abstract

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

Keywords

Stationary processmoment inequalitystrongly ergodic Markov chaindynamical systemempirical distributioninvariance principle

MSC classification

Secondary: 60G10: Stationary processes 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60F17: Functional limit theorems; invariance principles 28D05: Measure-preserving transformations 62G20: Asymptotic properties
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 1086 - 1096
Copyright
Copyright © Applied Probability Trust 2008 

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