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.Comment: 14 pages, REVTeX, 5 figures PostScrip