Titre :

Non-central limit theorem for the cubic variation of a class of selfsimilar stochastic processes

Auteur(s) :

Es-Sebaiy, Khalifa [Auteur]
Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) [SAMM]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

SIAM Theory of Probability and its Applications

Pagination :

1-23

Éditeur :

Society for Industrial and Applied Mathematics

Date de publication :

2010

ISSN :

1095-7219

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [en]

By using multiple Wiener-Itô stochastic integrals, we study the cubic variation of a class of selfsimilar stochastic processes with stationary increments (the Rosenblatt process with selfsimilarity order $H\in (\frac{1}{2}, ...
Lire la suite >By using multiple Wiener-Itô stochastic integrals, we study the cubic variation of a class of selfsimilar stochastic processes with stationary increments (the Rosenblatt process with selfsimilarity order $H\in (\frac{1}{2}, 1)$). This study is motivated by statistical purposes. We prove that this renormalized cubic variation satisfies a non-central limit theorem and its limit is (in the $L^{2}(\Omega)$ sense) still the Rosenblatt process.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Commentaire :

To appear in "Theory of Probability and its Applications"

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL