Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Pointwise and uniform asymptotics of the Vervaat error process

Auteur(s):

Code(s) de Classification MSC:

Résumé: It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e., the integrated uniform Bahadur-Kiefer process properly normalized, behaves like the square of the uniform empirical process. We give a complete description of the strong and weak asymptotic behaviour in sup-norm of this representation of the Vervaat process and, likewise, we study also its pointwise asymptotic behaviour.

Mots Clés: Empirical process ; quantile process ; Bahadur-Kiefer process ; Vervaat process

Date: 2000-04-21

Prépublication numéro: PMA-588