Paper (*cross-listing*): cond-mat/0504025 
  Date: Fri, 1 Apr 2005 14:16:25 GMT   (255kb)
 Title: Point process model of 1/f noise versus a sum of Lorentzians
 Authors: B. Kaulakys, V. Gontis, and M. Alaburda
 Comments: 23 pages, 10 figures, to be published in Phys. Rev. E
 Subj-class: Statistical Mechanics; Disordered Systems and Neural Networks;  Data Analysis, Statistics and Probability; Adaptation and Self-Organizing  Systems; Statistics; Computational Engineering, Finance, and Science;  Neurons and Cognition
 We present a simple point process model of $1/f^{?beta}$ noise, covering
 different values of the exponent $?beta$. The signal of the model consists of
 pulses or events. The interpulse, interevent, interarrival, recurrence or
 waiting times of the signal are described by the general Langevin equation with
 the multiplicative noise and stochastically diffuse in some interval resulting
 in the power-law distribution. Our model is free from the requirement of a wide
 distribution of relaxation times and from the power-law forms of the pulses. It
 contains only one relaxation rate and yields $1/f^ {?beta}$ spectra in a wide
 range of frequency. We obtain explicit expressions for the power spectra and
 present numerical illustrations of the model. Further we analyze the relation
 of the point process model of $1/f$ noise with the Bernamont-Surdin-McWhorter
 model, representing the signals as a sum of the uncorrelated components. We
 show that the point process model is complementary to the model based on the
 sum of signals with a wide-range distribution of the relaxation times. In
 contrast to the Gaussian distribution of the signal intensity of the sum of the
 uncorrelated components, the point process exhibits asymptotically a power-law
 distribution of the signal intensity. The developed multiplicative point
 process model of $1/f^{?beta}$ noise may be used for modeling and analysis of
 stochastic processes in different systems with the power-law distribution of
 the intensity of pulsing signals.
 ( http://arXiv.org/abs/cond-mat/0504025 ,  255kb)

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