Stochastic nonlinear differential equation generating 1/f noise

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.

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References in corpus (4)

• Unified Scaling Law for Earthquakes
• The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times
• Modeling 1/f noise
• Autoregressive model of 1/f noise

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