Resumen
We propose a statistical index for measuring the fluctuations of a stochastic process @x. This index is based on the generalized Lorenz curves and (modified) Gini indices of econometric theory. When @x is a fractional Brownian motion with Hurst index @a@?(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 @a@?(0,34), @a=34, or @a@?(34,1). 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.