On mean central limit theorems for stationary sequences

Dedecker, Jérôme; Rio, Emmanuel

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.

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