Occupancy Schemes Associated to Yule Processes

Abstract : An occupancy problem with an infinite number of bins and a random probability vector for the locations of the balls is considered. The respective sizes of bins are related to the split times of a Yule process. The asymptotic behavior of the landscape of first empty bins, i.e., the set of corresponding indices represented by point processes, is analyzed and convergences in distribution to mixed Poisson processes are established. Additionally, the influence of the random environment, the random probability vector, is analyzed. It is represented by two main components: an i.i.d.\ sequence and a fixed random variable. Each of these components has a specific impact on the qualitative behavior of the stochastic model. It is shown in particular that for some values of the parameters, some rare events, which are identified, play an important role on average values of the number of empty bins in some regions.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

Littérature citée [23 références]  Voir  Masquer  Télécharger

Contributeur : Philippe Robert <>
Soumis le : vendredi 17 octobre 2008 - 09:19:05
Dernière modification le : vendredi 16 février 2018 - 15:40:07
Document(s) archivé(s) le : lundi 7 juin 2010 - 20:24:02


Fichiers produits par l'(les) auteur(s)


  • HAL Id : inria-00331511, version 1
  • ARXIV : 0810.3079



Philippe Robert, Florian Simatos. Occupancy Schemes Associated to Yule Processes. 2008. 〈inria-00331511〉



Consultations de la notice


Téléchargements de fichiers