A Model for Persistent Levy Motion

TL;DR

This paper introduces a new model for persistent Levy motion that approximates fractional Levy noise and motion using stable probability laws and fractional calculus, suitable for Levy indices between 1 and 2.

Contribution

The paper presents a novel model based on Gnedenko's theorem and fractional calculus to approximate fractional Levy noise and motion, expanding modeling capabilities.

Findings

Model effectively approximates persistent Levy motion

Suitable for Levy index between 1 and 2

Demonstrates self-affine properties of the approximation

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.