Stochastic nonlinear differential equation generating 1/f noise
Statistical Mechanics
2009-11-10 v1 Spectral Theory
Chaotic Dynamics
Data Analysis, Statistics and Probability
Abstract
Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general Langevin equation with a multiplicative noise) that gives 1/f noise is derived for the first time. The solution of the equation exhibits the power-law distribution. The process with 1/f noise is demonstrated by the numerical solution of the derived equation with the appropriate restriction of the diffusion of the signal in some finite interval.
Keywords
Cite
@article{arxiv.cond-mat/0408507,
title = {Stochastic nonlinear differential equation generating 1/f noise},
author = {B. Kaulakys and J. Ruseckas},
journal= {arXiv preprint arXiv:cond-mat/0408507},
year = {2009}
}
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3 figures