| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
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