A model for persistent Levy motion

We propose a model, which allows us to approximate fractional Levy noise and fractional Levy motion. Our model is based on: (i) the Gnedenko limit theorem for an attraction basin of stable probability law, and (ii) fractional noise as a 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.