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Starting from the simple point process model of 1/f noise we derive astochastic nonlinear differential equation for the signal exhibiting 1/f noisein any desirably wide range of frequency. A stochastic differential equation(the general Langevin equation with a multiplicative noise) that gives 1/fnoise is derived for the first time. The solution of the equation exhibits thepower-law distribution. The process with 1/f noise is demonstrated by thenumerical solution of the derived equation with the appropriate restriction ofthe diffusion of the signal in some finite interval.Comment: 3 figure

physical review. e, statistical, nonlinear and soft matter physics

Stochastic nonlinear differential equation generating<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:math>noise

Stochastic nonlinear differential equation generating1∕fnoise