Coupled nonlinear stochastic differential equations generating arbitrary distributed observable with 1/f noise
Abstract
Nonlinear stochastic differential equations provide one of the mathematical models yielding 1/f noise. However, the drawback of a single equation as a source of 1/f noise is the necessity of power-law steady-state probability density of the signal. In this paper we generalize this model and propose a system of two coupled nonlinear stochastic differential equations. The equations are derived from the scaling properties necessary for the achievement of 1/f noise. The first equation describes the changes of the signal, whereas the second equation represents a fluctuating rate of change. The proposed coupled stochastic differential equations allows us to obtain 1/f spectrum in a wide range of frequencies together with the almost arbitrary steady-state density of the signal.
Cite
@article{arxiv.1603.03013,
title = {Coupled nonlinear stochastic differential equations generating arbitrary distributed observable with 1/f noise},
author = {J. Ruseckas and R Kazakevičius and B Kaulakys},
journal= {arXiv preprint arXiv:1603.03013},
year = {2016}
}