Abstract

We propose the model, which allows us to approximate fractional Levy noise and fractional Levy motion. Our model is based (i) on the Gnedenko limit theorem for an attraction basin of stable probability law, and (ii) on regarding fractional noise as the result of fractional integration/differentiation of a white Levy noise. We investigate self- affine properties of the approximation and conclude that it is suitable for modeling persistent Levy motion with the Levy index between 1 and 2. PACS number(s): 02.50.-r, 05.40.+j Typeset using REVTEX 1 I. INTRODUCTION. By Levy motions, or Levy processes, we designate a class of random functions, which are a natural generalization of the Brownian motion, and whose increments are stationary, statistically self-affine and stably distributed in the sense of P. Levy [1]. Two important subclasses are (i) the stable processes, or the ordinary Levy motions, which generalize the

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