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

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

Strong approximations of three-dimensional Wiener sausages


Code(s) de Classification MSC:

Résumé: In this paper we prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall [10]'s fine $L^2$-norm estimates between the Wiener sausage and the Brownian intersection local times.

Mots Clés: Wiener sausage ; intersection local times ; strong approximation

Date: 2004-05-07

Prépublication numéro: PMA-909