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

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