A Model for Ordinary Levy Motion

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. PACS number(s): 02.50.-r, 05.40.+j By Levy motions, or Levy processes, one designates a class of random functions, which are a natural generalization of the Brownian motions, and whose increments are stably distributed in the sense of P. Levy[1]. Two important subclasses are (i) ordinary Levy motions (oLm’s), which generalize the ordinary Brownian motion, or the Wiener process [2], and whose increments are independent, and (ii) fractional Levy motions (fLm’s), which generalize the fractional Brownian motions (fBm’s) [3] and have an infinite span of interdependence. The Levy random processes play an important role in different areas of applications, e.g., in economy [4], biology and physiology [5], fractal and multifractal analysis [6], problems of anomalous diffusion [7] etc. In this