Phys. Rev. E 70, 020101(R) (2004) [3 pages]Stochastic nonlinear differential equation generating 1∕f noise
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. © 2004 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.70.020101
DOI:
10.1103/PhysRevE.70.020101
PACS:
05.40.−a, 72.70.+m, 89.75.Da
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