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Empirical Processes of Multidimensional Systems with Multiple Mixing Properties

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00474313
Contributor : Olivier Durieu <>
Submitted on : Monday, April 19, 2010 - 4:03:29 PM
Last modification on : Saturday, November 24, 2018 - 1:21:59 AM

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Herold Dehling, Olivier Durieu. Empirical Processes of Multidimensional Systems with Multiple Mixing Properties. Stochastic Processes and their Applications, Elsevier, 2011, 121 (5), pp.1076-1096. ⟨10.1016/j.spa.2011.01.010⟩. ⟨hal-00474313⟩

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