Journal of Applied Probability

A fourth moment inequality for functionals of stationary processes

Olivier Durieu

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Abstract

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.

Article information

Source
J. Appl. Probab. Volume 45, Number 4 (2008), 1086-1096.

Dates
First available in Project Euclid: 7 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.jap/1231340235

Digital Object Identifier
doi:10.1239/jap/1231340235

Mathematical Reviews number (MathSciNet)
MR2484163

Zentralblatt MATH identifier
1157.60029

Subjects
Primary: 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

Keywords
Stationary process moment inequality strongly ergodic Markov chain dynamical system empirical distribution invariance principle

Citation

Durieu, Olivier. A fourth moment inequality for functionals of stationary processes. J. Appl. Probab. 45 (2008), no. 4, 1086--1096. doi:10.1239/jap/1231340235. https://projecteuclid.org/euclid.jap/1231340235.


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