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Stochastic nonlinear differential equation generating 1/f noise
1Institute of Theoretical Physics and Astronomy, Vilnius University, A. Gostauto 12, LT-01108 Vilnius, Lithuania. kaulakys@itpa.lt
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. 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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