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

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

On random sets connected to the partial records of Poisson point process

Auteur(s):

Code(s) de Classification MSC:

Résumé: Random intervals are constructed from partial records in a Poisson point process in $]0,\infty[\times]0,\infty[.$ These are used to cover partially $[0,\infty[$; the purpose of this work is to study the random set $\Rs$ that is left uncovered. We show that $\Rs$ enjoys the regenerative property and identify its distribution in terms of the characteristics of the Poisson point process. As an application we show that $\Rs$ is almost surely a fractal set and we calculate its dimension.

Mots Clés: Poisson point process ; Extremal Process ; Regenerative sets ; Subordinators ; Fractal dimensions

Date: 2001-06-26

Prépublication numéro: PMA-674