A moment approach to non-Gaussian colored noises

TL;DR

This paper develops a second-order moment approach to analyze non-Gaussian colored noises in Langevin systems, deriving effective equations and stationary distributions that agree well with simulations and other methods.

Contribution

The authors introduce a novel second-order moment method for non-Gaussian colored noises, providing accurate stationary distributions and dynamical insights.

Findings

The derived probability distribution matches direct simulations.

The moment method outperforms some existing approximation methods.

Dynamical properties under external input are effectively analyzed.

Abstract

The Langevin system subjected to non-Gaussian noise has been discussed, by using the second-order moment approach with two kinds of models for generating the noise. We have derived the effective differential equation (DE) for a variable $x$, from which the stationary probability distribution $P(x)$ has been calculated with the use of the Fokker-Planck equation. The result of $P(x)$ calculated by the moment method is compared to several expressions obtained by different methods such as the universal colored noise approximation (UCNA) [Jung and H\"{a}nggi, Phys. Rev. A {\bf 35}, 4464 (1987)] and the functional-integral method. It has been shown that our $P(x)$ is in good agreement with that of direct simulations (DSs). We have also discussed dynamical properties of the model with an external input, solving DEs in the moment method.