On mean central limit theorems for stationary sequences

Abstract

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.

Published in at http://dx.doi.org/10.1214/07-AIHP117 the Annales de l'Institut Henri Poincaré - Probabilités et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Rate of convergence in the multidimensional central limit theorem for stationary processes. Application to the Knudsen gas and to the Sinai billiard

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