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) |
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