Large Deviation Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments

Abstract : We consider a family of stochastic processes built from infinite sums of independent positive random functions on R+. Each of these functions increases linearly between two consecutive negative jumps, with the jump points following a Poisson point process on R+. The motivation for studying these processes stems from the fact that they constitute simplified models for TCP traffic. Such processes bear some analogy with L'evy processes, but are more complex since their increments are neither stationary nor independent. In [3], the Hausdorf multifractal spectrum of these processes were computed. We are interested here in their Large Deviation and Legendre multifractal spectra. These "statistical" spectra are seen to give, in this case, a richer information than the "geometrical" Hausdorf spectrum. In addition, our results provide a firm theoretical basis for the empirical discovery of the multifractal nature of TCP traffic.
Type de document :
Article dans une revue
IEEE/ACM Transactions on Networking, IEEE/ACM, 2013, 21 (4), pp.1309-1321. 〈10.1109/tnet.2012.2229469 〉
Liste complète des métadonnées

Littérature citée [27 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00633195
Contributeur : Lisandro Fermin <>
Soumis le : lundi 22 octobre 2012 - 16:02:47
Dernière modification le : mardi 16 janvier 2018 - 15:38:31
Document(s) archivé(s) le : mercredi 23 janvier 2013 - 03:43:15

Fichier

v12.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Jacques Lévy Véhel, Michal Rams. Large Deviation Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments. IEEE/ACM Transactions on Networking, IEEE/ACM, 2013, 21 (4), pp.1309-1321. 〈10.1109/tnet.2012.2229469 〉. 〈inria-00633195v2〉

Partager

Métriques

Consultations de la notice

249

Téléchargements de fichiers

178