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

CNRS U.M.R. 7599
| ||

``Probabilités et Modèles Aléatoires''
| ||

**Auteur(s): **

**Code(s) de Classification MSC:**

- 60F05 Central limit and other weak theorems
- 60F17 Functional limit theorems; invariance principles

**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*