| Université Paris 6 Pierre et Marie Curie | Université Paris 7 Denis Diderot | |
| CNRS U.M.R. 7599 | ||
| ``Probabilités et Modèles Aléatoires'' | ||
Auteur(s):
Code(s) de Classification MSC:
Résumé: We propose a statistical index for measuring the fluctuations of a stochastic process $\xi$. This index is based on the generalized Lorenz curves and (modified) Gini indices of econometric theory. When $\xi$ is a fractional Brownian motion with Hurst index $\alpha\in(0,1)$, we develop a complete picture of the asymptotic theory of our index. In particular, we show that the asymptotic behaviour of our proposed index depends critically on whether $0<\alpha<3/4$, $\alpha=3/4$, or $3/4<\alpha<1$. Furthermore, in the first two cases, there is a Gaussian limit law, while the third case has an explicit limit law that is in the second Wiener chaos.
Mots Clés: Convex rearrangements ; Lorenz curves ; Gini indices ; fractional Brownian motion
Date: 2003-06-04
Prépublication numéro: PMA-825