Stochastic nonlinear differential equation generating 1/f noise

Details Stochastic nonlinear differential equation generating 1/f noise Stochastic nonlinear differential equation generating 1/f noise

2004-08-24

arxiv.org/abs/cond-mat/0408507v1

Phys. Rev. E, 020101(R), 70 (2), (2004)

Physics

Condensed Matter

Statistical Mechanics

3 figures

Scientific paper

10.1103/PhysRevE.70.020101

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.

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