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

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

A new maximal inequality and invariance principle for stationary sequences

Auteur(s):

Code(s) de Classification MSC:

Résumé: We derive a new maximal inequality for stationary sequences under a martingale-type condition introduced by Maxwell and Woodroofe (2000). Then, we apply it to establish the Donsker invariance principle for this class of stationary sequences. A Markov chain example is given in order to show the optimality of the conditions imposed.

Mots Clés: asymptotic normality ; ergodic theorem ; functional central limit theorem ; invariance principle ; martingale ; maximal inequality ; Markov chains ; renewal sequences

Date: 2003-05-14

Prépublication numéro: PMA-819