Self - affinity of ordinary Levy motion, spurious multi - affinity and pseudo - Gaussian relations
Abstract
The ordinary Levy motion is a random process whose stationary independent increments are statistically self-affine and distributed with a stable probability law characterized by the Levy index alpha, 0 < alpha < 2. The divergence of statistical moments of the order q > alpha leads to an important role of the finite sample effects. The objective of this paper is to study the influence of these effects on the self-affine properties of the ordinary Levy motion, namely, on the '1/alpha laws', that is, time dependence of the q-th order structure function and of the range. Analytical estimates and simulations of the finite sample effects clearly demonstrates three phenomena: spurious multi-affinity of the Levy motion, strong dependence of the structure function on the sample size at q > alpha, and pseudo-Gaussian behavior of the second-order structure function and of the normalized range. We discuss these phenomena in detail and propose the modified Hurst method for empirical rescaled range analysis.
Cite
@article{arxiv.cond-mat/9907234,
title = {Self - affinity of ordinary Levy motion, spurious multi - affinity and pseudo - Gaussian relations},
author = {A. V. Chechkin and V. Yu. Gonchar},
journal= {arXiv preprint arXiv:cond-mat/9907234},
year = {2007}
}
Comments
13 pages, RevTeX 3.0, 7 figures PostScript