Title :

Asymptotic normality for a modified quadratic variation of the Hermite process

Author(s) :

Ayache, Antoine [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Bernoulli

Publication date :

2024

English keyword(s) :

60H15 60H07 60G35 Hermite process fractional Brownian motion parameter estimation multiple Wiener-Itô integrals Stein-Malliavin calculus strong consistency asymptotic normality Ornstein-Uhlenbeck process Hurst index estimation
60H15
60H07
60G35 Hermite process
fractional Brownian motion
parameter estimation
multiple Wiener-Itô integrals
Stein-Malliavin calculus
strong consistency
asymptotic normality
Ornstein-Uhlenbeck process
Hurst index estimation

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]

English abstract : [en]

We consider a modified quadratic variation of the Hermite process based on some well-chosen increments of this process. These special increments have the very useful property to be independent and identically distributed ...
Show more >We consider a modified quadratic variation of the Hermite process based on some well-chosen increments of this process. These special increments have the very useful property to be independent and identically distributed up to asymptotically negligible remainders. We prove that this modified quadratic variation satisfies a Central Limit Theorem and we derive its rate of convergence under the Wasserstein distance via Stein-Malliavin calculus. As a consequence, we construct, for the first time in the literature related to Hermite processes, a strongly consistent and asymptotically normal estimator for the Hurst parameter.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Analyse stochastique et déterministe pour des modèles irréguliers

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL