# New Techniques for Empirical Process of Dependent Data

Abstract : We present a new technique for proving empirical process invariance principle for stationary processes $(X_n)_{n\geq 0}$. The main novelty of our approach lies in the fact that we only require the central limit theorem and a moment bound for a restricted class of functions $(f(X_n))_{n\geq 0}$, not containing the indicator functions. Our approach can be applied to Markov chains and dynamical systems, using spectral properties of the transfer operator. Our proof consists of a novel application of chaining techniques.
Type de document :
Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2009, 119, pp.3699-3718. 〈10.1016/j.spa.2009.07.003〉
Domaine :

https://hal.archives-ouvertes.fr/hal-00291501
Contributeur : Olivier Durieu <>
Soumis le : vendredi 27 juin 2008 - 11:28:53
Dernière modification le : mardi 5 juin 2018 - 10:14:09

### Citation

Herold Dehling, Olivier Durieu, Dalibor Volný. New Techniques for Empirical Process of Dependent Data. Stochastic Processes and their Applications, Elsevier, 2009, 119, pp.3699-3718. 〈10.1016/j.spa.2009.07.003〉. 〈hal-00291501〉

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