Journal of Applied Probability
- J. Appl. Probab.
- Volume 45, Number 4 (2008), 1086-1096.
A fourth moment inequality for functionals of stationary processes
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.
J. Appl. Probab. Volume 45, Number 4 (2008), 1086-1096.
First available in Project Euclid: 7 January 2009
Permanent link to this document
Digital Object Identifier
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
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.