Governing stochastic equation for a self-similar random process

V.P. Koverda and V.N. Skokov

Physica A: Statistical Mechanics and its Applications, 2023, vol. 628, issue C

Abstract: A stochastic differential equation is proposed, the solution of which is a characteristic random function that describes a stochastic process with Gaussian tails of distribution functions. The reciprocal to the characteristic random function describes a self-similar random process with a power spectrum inversely proportional to the frequency and with power-law a behavior of tails in the amplitude distribution functions. 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; Noise; Maximum entropy (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:628:y:2023:i:c:s0378437123006969

DOI: 10.1016/j.physa.2023.129141

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