Journal of Applied Probability

A fourth moment inequality for functionals of stationary processes

Olivier Durieu

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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.

Article information

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

First available in Project Euclid: 7 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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