Strongly super-Poisson statistics replaced by a wide-pulse Poisson process: The billiard random generator

Olga A. Chichigina and Davide Valenti

Chaos, Solitons & Fractals, 2021, vol. 153, issue P1

Abstract: In this paper we present a study on random processes consisting of delta pulses characterized by strongly super-Poisson statistics and calculate its spectral density. We suggest a method for replacing a strongly super-Poisson process with a wide-pulse Poisson process, while demonstrating that these two processes can be set in such a way to have similar spectral densities, the same mean values, and the same correlation times. We also present a billiard system that can be used to generate random pulse noise of arbitrary statistical properties. The particle dynamics is considered in terms of delta and wide pulses simultaneously. The results of numerical experiments with the billiard system are in a good agreement with the analytical findings.

Keywords: Renewal process; Fluctuation phenomena; Stochastic processes; Billiard-like systems; Super-Poisson statistics; Hardware random number generator (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921008055

DOI: 10.1016/j.chaos.2021.111451

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