Titre :

Asymptotic behavior of the quadratic variation of the sum of two Hermite processes of consecutive orders

Auteur(s) :

Clausel, Marianne [Auteur]
Statistique Apprentissage Machine [SAM]
Roueff, François [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Taqqu, Murad [Auteur]
Department of Mathematics and Statistics [Boston]
Tudor, Ciprian A. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Stochastic Processes and their Applications

Pagination :

2517-2541

Éditeur :

Elsevier

Date de publication :

2014-07

ISSN :

0304-4149

Mot(s)-clé(s) en anglais :

Hermite processes
quadratic variation
covariation
Wiener chaos
self-similar processes
long--range dependence

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [en]

Hermite processes are self--similar processes with stationary increments which appear as limits of normalized sums of random variables with long range dependence. The Hermite process of order $1$ is fractional Brownian ...
Lire la suite >Hermite processes are self--similar processes with stationary increments which appear as limits of normalized sums of random variables with long range dependence. The Hermite process of order $1$ is fractional Brownian motion and the Hermite process of order $2$ is the Rosenblatt process. We consider here the sum of two Hermite processes of order $q\geq 1$ and $q+1$ and of different Hurst parameters. We then study its quadratic variations at different scales. This is akin to a wavelet decomposition. We study both the cases where the Hermite processes are dependent and where they are independent. In the dependent case, we show that the quadratic variation, suitably normalized, converges either to a normal or to a Rosenblatt distribution, whatever the order of the original Hermite processes.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL