One-dimensional space-discrete transport subject to Levy perturbations

TL;DR

This paper analyzes a one-dimensional discrete transport equation influenced by Levy noise, revealing how the stationary covariance structure behaves under different Levy perturbations and highlighting differences from continuous systems.

Contribution

It provides explicit solutions for the discrete transport equation with Levy forcing and explores the invariance of covariance structures under various Levy perturbations.

Findings

Covariance invariance for Levy perturbations with finite second moment

Differences between discrete and continuous systems in solution properties

Analytic solutions enable detailed study of Levy-driven transport

Abstract

In this paper we study a one-dimensional space-discrete transport equation subject to additive Levy forcing. The explicit form of the solutions allows their analytic study. In particular we discuss the invariance of the covariance structure of the stationary distribution for Levy perturbations with finite second moment. The situation of more general Levy perturbations lacking the second moment is considered as well. We moreover show that some of the properties of the solutions are pertinent to a discrete system and are not reproduced by its continuous analogue.