arXiv subjects

Miglius Alaburda

Publications and source records attributed to Miglius Alaburda.

2 recordsLinked to original sources

arXiv2005

Modeling of flows with the power-law spectral densities and power-law distributions of flow's intensities

We present analytical and numerical results of modeling of flows represented as the correlated non-Poissonian point process and as the Poissonian sequence of pulses of the different size. Both models may generate signals with the power-law distributions of the intensity of the flow and the power-law spectral density. Furthermore, different distributions of the interevent time of the point process and different statistics of the size of pulses may result in $1/f^β$ noise (one-over-f noise, 1-f noise) with $0.5\lesssimβ\lesssim2$. Combination of the models is applied for modeling of the Internet traffic.

physics.soc-ph↗

arXiv2005

Nonlinear stochastic models of 1/f noise and power-law distributions

Starting from the developed generalized point process model of $1/f$ noise (B. Kaulakys et al, Phys. Rev. E 71 (2005) 051105; cond-mat/0504025) we derive the nonlinear stochastic differential equations for the signal exhibiting 1/f^β$ noise and $1/x^λ$ distribution density of the signal intensity with different values of $β$ and $λ$. The processes with $1/f^β$ are demonstrated by the numerical solution of the derived equations with the appropriate restriction of the diffusion of the signal in some finite interval. The proposed consideration may be used for modeling and analysis of stochastic processes in different systems with the power-law distributions, long-range memory or with the elements of self-organization.

cond-mat.stat-mech↗