Central limit theorem under the Dedecker-Rio condition in some Banach spaces
Résumé
We extend the central limit theorem under the Dedecker-Rio condition to adapted stationary and ergodic sequences of random variables taking values in a class of smooth Banach spaces. This result applies to the case of random variables taking values in Lp(μ), with 2 ⩽ p < ∞ and μ a σ-finite real measure. As an application we give a sufficient condition for empirical processes indexed by Sobolev balls to satisfy the central limit theorem, and discuss about the optimality of these conditions.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
---|