Characteristic function of a self-similar random process

V. P. Koverda, V. N. Skokov

Institute of Thermal Physics, Ural Branch, Russian Academy of Sciences, Ekaterinburg, Yekaterinburg, Russia

Abstract: A stochastic differential equation is proposed for a characteristic function whose inverse function describes a self-similar random process with a power-law behavior of power spectra in a wide frequency range and a power-law amplitude distribution function. Gaussian “tails” for the characteristic distribution make it possible to evaluate its stability according to the formulas of classical statistics using the maximum of the Gibbs-Shannon entropy and, therefore, the stability of a random process given by an inverse function.

Keywords: self-similar random processes, stochastic equations, power spectrum, $1/f$-noise, maximum entropy.

Received: 08.04.2022
Revised: 08.04.2022
Accepted: 23.05.2022

DOI: 10.21883/PJTF.2022.14.52861.19221

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