On mean central limit theorems for stationary sequences

Jérôme Dedecker (1) , Emmanuel Rio (2, 3)

1 LSTA - Laboratoire de Statistique Théorique et Appliquée
2 ALEA - Advanced Learning Evolutionary Algorithms
3 LMV - Laboratoire de Mathématiques de Versailles

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.

Domaines: Probabilités [math.PR]

Jérôme Dedecker, Emmanuel Rio. On mean central limit theorems for stationary sequences. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2008, 44 (4), pp.693-726. ⟨10.1214/07-AIHP117⟩. ⟨hal-00672866⟩