Universités de Paris 6 & Paris 7 - CNRS ( UMR 7599 ) PRÉPUBLICATIONS DU LABORATOIRE
نویسندگان
چکیده
We propose a statistical index for measuring the fluctuations of a stochastic process ξ. This index is based on the generalized Lorenz curves and (modified) Gini indices of econometric theory. When ξ is a fractional Brownian motion with Hurst index α ∈ (0, 1), we develop a complete picture of the asymptotic theory of our index. In particular, we show that the asymptotic behavior of our proposed index depends critically on whether α ∈ (0, 3 4), α = 3 4 , or α ∈ (3 4 , 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.
منابع مشابه
Universités de Paris 6 & Paris 7 - CNRS ( UMR 7599 ) PRÉPUBLICATIONS DU LABORATOIRE DE PROBABILITÉS & MODÈLES ALÉATOIRES
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