Function-indexed empirical processes based on an infinite source Poisson transmission stream

François Roueff 1 Gennady Samorodnitsky 2 Philippe Soulier 3
1 LTCI - Laboratoire Traitement et Communication de l'Information
2 ORIE - School of Operations Research and Information Engineering
3 MODAL'X - Modélisation aléatoire de Paris X
Abstract : We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the function, the normalized fluctuations of such an empirical process converge to a non-Gaussian stable process. This phenomenon can be viewed as caused by the long-range dependence in the transmission process. Completing previous results on the empirical mean of similar types of processes, our results on non-linear bounded functions exhibit the influence of the limit transmission rate distribution at high session lengths on the asymptotic behavior of the empirical process. As an illustration, we apply the main result to estimation of the distribution function of the steady state value of the transmission process.
Mots-clés : empirical process M/G queue shot noise long range dependence
Type de document :
Article dans une revue
Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2012, pp.783-802. 〈10.3150/11-BEJ367〉
Liste complète des métadonnées
https://hal-imt.archives-ouvertes.fr/hal-00471634
Contributeur : François Roueff <>
Soumis le : lundi 9 juillet 2012 - 16:24:38
Dernière modification le : mercredi 4 juillet 2018 - 23:14:02
Document(s) archivé(s) le : mercredi 10 octobre 2012 - 04:05:11

Fichiers

bej367.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

INSMI | PARISTECH | TELECOM-PARISTECH | MODALX

Citation

François Roueff, Gennady Samorodnitsky, Philippe Soulier. Function-indexed empirical processes based on an infinite source Poisson transmission stream. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2012, pp.783-802. 〈10.3150/11-BEJ367〉. 〈hal-00471634v3〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

360

Téléchargements de fichiers

99

Contact

support.ccsd.cnrs.fr
hal.support@ccsd.cnrs.fr
Logo CCSD