Title :

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

Author(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]

Journal title :

Stochastic Processes and their Applications

Pages :

2517-2541

Publisher :

Elsevier

Publication date :

2014-07

ISSN :

0304-4149

English keyword(s) :

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

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL