Correlated L\'evy noise in linear dynamical systems

TL;DR

This paper investigates linear dynamical systems influenced by correlated Levy noise, analyzing their properties, solving the associated Fokker-Planck equation, and discussing the effects of noise correlation and approximation methods.

Contribution

It introduces a model of Levy noise in linear systems, analyzes correlation properties, and solves the Fokker-Planck equation for such noise, expanding understanding of non-white Levy-driven processes.

Findings

Distributions retain Levy shape with smaller width than white noise case

Correlation properties of Levy noise are characterized

Adiabatic approximation applicability is discussed

Abstract

Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit. Applicability of the adiabatic approximation in the case of the linear force is discussed.