Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

On the weak invariance principle of stationary sequences under projective criteria

Auteur(s):

Code(s) de Classification MSC:

Résumé: In this paper we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. For the sake of applications, we also give sufficient conditions involving the conditional expectation of one, or two random variables with respect to the distant past. The results are sharp and contribute to the clarification of the central limit theorem question for stationary sequences.

Mots Clés: Central limit theorem ; weak invariance principle ; projective criteria ; strong mixing sequences ; martingale approximation

Date: 2003-05-27

Prépublication numéro: PMA-823