Agenda de l’IDP

Séminaire SPACE Tours

An estimation of the self-similarity and the stability indices of a H-self-similar stable process
Thi To Nhu DANG (Da Nang, Vietnam)
Friday 03 May 2019 10:30 -  Tours -  E 1180

Résumé :

The aim of this work is to construct consistent estimators of the self-similar index H and the stable index α of a H-sssi (self-similar stationary increments) symmetric α− stable (SαS) process, using a framework of negative power variations. More precisely, let X be a H-sssi SαS process. The process X is observed at points k/n , k = 0, . . . , n. In the view of the fact that a stable random variable has a density function, β−negative power variations have expectations and covariances for − 1/2 < β < 0. Our estimate is based on these variations.This new approach provides estimators of H and α without the assumptions on the existence moment of the underlying processes.
It also allows us to give the estimators of H and α separately.
We obtain consistent estimators, with rate of convergence, for several classical H-sssi α-stable processes (fractional Brownian motion, well-balanced linear fractional stable motion, Takenaka’s process, L ́evy motion). Moreover, we obtain asymptotic normality of our estimators for fractional Brownian motion and L ́evy motion.
This is a joint work with Jacques Istas (LJK, Grenoble)



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