A Model for Ordinary Levy Motion

Abstract

We propose a simple model based on the Gnedenko limit theorem for simulation and studies of the ordinary Levy motion, that is, a random process, whose increments are independent and distributed with a stable probability law. We use the generalized structure function for characterizing anomalous diffusion rate and propose to explore the modified Hurst method for empirical rescaled range analysis. We also find that the structure function being estimated from the ordinary Levy motion sample paths as well as the (ordinary) Hurst method lead to spurious ''pseudo-Gaussian'' relations.