Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

On mean central limit theorems for stationary sequences

Jérôme Dedecker and Emmanuel Rio

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In this paper, we give estimates of the minimal ${\mathbb{L}}^{1}$ 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.


Dans cet article, nous donnons des majorations de la distance minimale ${\mathbb{L}}^{1}$ 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.

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Ann. Inst. H. Poincaré Probab. Statist., Volume 44, Number 4 (2008), 693-726.

First available in Project Euclid: 5 August 2008

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Primary: 60F05: Central limit and other weak theorems

Mean central limit theorem Wasserstein distance Minimal distance Martingale difference sequences Strong mixing Stationary sequences Weak dependence Rates of convergence Projective criteria


Dedecker, Jérôme; Rio, Emmanuel. On mean central limit theorems for stationary sequences. Ann. Inst. H. Poincaré Probab. Statist. 44 (2008), no. 4, 693--726. doi:10.1214/07-AIHP117.

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