1/f noise from nonlinear stochastic differential equations
Adaptation and Self-Organizing Systems
2015-05-18 v1 Data Analysis, Statistics and Probability
Abstract
We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/f^b noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/f^b noise, and provides further insights into the origin of 1/f^b noise.
Cite
@article{arxiv.1002.4316,
title = {1/f noise from nonlinear stochastic differential equations},
author = {J. Ruseckas and B. Kaulakys},
journal= {arXiv preprint arXiv:1002.4316},
year = {2015}
}