Titre :

Hermite variations of the fractional Brownian sheet

Auteur(s) :

Réveillac, Anthony [Auteur]
Institut für Mathematik [Berlin]
Stauch, Michael [Auteur]
Institut für Mathematik [Berlin]
Tudor, Ciprian A. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Mot(s)-clé(s) en anglais :

Limit theorems
Hermite variations
Multiple stochastic integrals
Malliavin calculus
Weak convergence

Discipline(s) HAL :

Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [en]

We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet $W^{\alpha, \beta}$ with Hurst parameter $(\alpha, \beta) \in (0,1)^2$. When $0<\alpha \leq 1-\frac{1}{2q}$ ...
Lire la suite >We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet $W^{\alpha, \beta}$ with Hurst parameter $(\alpha, \beta) \in (0,1)^2$. When $0<\alpha \leq 1-\frac{1}{2q}$ or $0<\beta \leq 1-\frac{1}{2q}$ a central limit theorem holds for the renormalized Hermite variations of order $q\geq 2$, while for $1-\frac{1}{2q}<\alpha, \beta < 1$ we prove that these variations satisfy a non-central limit theorem. In fact, they converge to a random variable which is the value of a two-parameter Hermite process at time $(1,1)$.Lire moins >

Langue :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL