On mean central limit theorems for stationary sequences

Dedecker, Jérôme; Rio, Emmanuel

Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 4, pp. 693-726.

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.

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.

Classification: 60F05
Keywords: 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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