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| HAL : hal-00471634, version 3 |
| arXiv : 1004.2182 |
| DOI : 10.3150/11-BEJ367 |
| Fiche détaillée |  Récupérer au format |
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| Bernoulli (2012) 783-802 |
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| Versions disponibles : | v1 (13-04-2010) | v2 (15-10-2010) | v3 (10-07-2012) |
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| Function-indexed empirical processes based on an infinite source Poisson transmission stream |
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| François Roueff 1Gennady Samorodnitsky 2 |
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| ANR MATAIM Collaboration(s) |
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| (01/08/2012) |
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| 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. |
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| 1 : | Laboratoire Traitement et Communication de l'Information [Paris] (LTCI) |
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Télécom ParisTech – CNRS : UMR5141 |
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| 2 : | School of Operations Research and Information Engineering (ORIE) |
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Cornell University |
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| 3 : | Modélisation aléatoire de Paris X (MODAL'X) |
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Université Paris X - Paris Ouest Nanterre La Défense |
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| Domaine | : | Mathématiques/Probabilités |
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| empirical process – M/G queue – shot noise – long range dependence |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00471634, version 3 | |
| http://hal-institut-mines-telecom.archives-ouvertes.fr/hal-00471634 | |
| oai:hal-institut-mines-telecom.archives-ouvertes.fr:hal-00471634 | |
| Contributeur : François Roueff | |
| Soumis le : Lundi 9 Juillet 2012, 16:24:38 | |
| Dernière modification le : Mardi 10 Juillet 2012, 08:45:40 | |
