Title :

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

Author(s) :

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

Journal title :

SIAM Theory of Probability and its Applications

Pages :

1-23

Publisher :

Society for Industrial and Applied Mathematics

Publication date :

2010

ISSN :

1095-7219

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

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

Language :

Anglais

Popular science :

Non

Comment :

To appear in "Theory of Probability and its Applications"

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL