HAL : hal-00474313, version 1

arXiv : 1004.1088

DOI : 10.1016/j.spa.2011.01.010

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Stochastic Processes and their Applications 121, 5 (2011) 1076-1096

Empirical Processes of Multidimensional Systems with Multiple Mixing Properties

Herold Dehling, Olivier Durieu 1

(2011)

We establish a multivariate empirical process central limit theorem for stationary $\R^d$-valued stochastic processes $(X_i)_{i\geq 1}$ under very weak conditions concerning the dependence structure of the process. As an application we can prove the empirical process CLT for ergodic torus automorphisms. Our results also apply to Markov chains and dynamical systems having a spectral gap on some Banach space of functions. Our proof uses a multivariate extension of the techniques introduced by Dehling, Durieu and Volný \cite{DehDurVol09} in the univariate case. As an important technical ingredient, we prove a $(2p)$th moment bound for partial sums in multiply mixing systems.

1 :	Laboratoire de Mathématiques et Physique Théorique (LMPT)
	CNRS : UMR6083 – Université François Rabelais - Tours

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:

Mathématiques/Probabilités Mathématiques/Systèmes dynamiques

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Contributeur : Olivier Durieu <>

Soumis le : Lundi 19 Avril 2010, 16:03:29

Dernière modification le : Vendredi 1 Février 2013, 11:29:38