Fractional Levy motion through path integrals

TL;DR

This paper derives the propagator for fractional Levy motion using path integral methods, generalizing known results for Brownian and fractional Brownian motions, and also obtains the associated fractional diffusion equation.

Contribution

It provides an explicit derivation of the propagator for fractional Levy motion, extending the path integral approach to this class of self-similar stochastic processes.

Findings

Derived the propagator of fractional Levy motion.

Recovered propagators of Brownian and fractional Brownian motions as special cases.

Obtained the fractional diffusion equation for fLm.

Abstract

Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The fractional diffusion equation corresponding to fLm is also obtained.