On mean central limit theorems for stationary sequences
Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 4, pp. 693-726.

Dans cet article, nous donnons des majorations de la distance minimale 𝕃 1 entre la loi de la somme normalisée et sa loi limite gaussienne pour des suites stationnaires satisfaisant des critères projectifs à la Gordin ou des conditions de dépendance faible.

In this paper, we give estimates of the minimal 𝕃 1 distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.

DOI : 10.1214/07-AIHP117
Classification : 60F05
Mots-clés : mean central limit theorem, Wasserstein distance, minimal distance, martingale difference sequences, strong mixing, stationary sequences, weak dependence, rates of convergence, projective criteria 
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Dedecker, Jérôme; Rio, Emmanuel. On mean central limit theorems for stationary sequences. Annales de l'I.H.P. Probabilités et statistiques, Tome 44 (2008) no. 4, pp. 693-726. doi : 10.1214/07-AIHP117. http://www.numdam.org/articles/10.1214/07-AIHP117/

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