Fractional Levy motion through path integrals

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.

9 pages, minor changes, published version

References in corpus (1)

• Path integral formulation of fractional Brownian motion for general Hurst exponent

Cited by in corpus (3)

• Path Integral Formulation for Lévy Flights - Evaluation of the Propagator for Free, Linear and Harmonic Potentials in the Over- and Underdamped Limits
• On the kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts
• Path integrals for fractional Brownian motion and fractional Gaussian noise