Universal Poisson-process limits for general random walks

Iddo Eliazar

Physica A: Statistical Mechanics and its Applications, 2018, vol. 512, issue C, 1160-1174

Abstract: This paper considers ensembles of general, independent and identically distributed, random walks. Taking the ensemble-size to grow infinitely large, and also taking the running-time of the random walks to grow infinitely large, universal Poisson-process limits are obtained. Specifically, it is established that the positions of general linear random walks converge universally to Poisson processes, over the real line, with uniform and exponential intensities. And, it is established that the positions of general geometric random walks converge universally to Poisson processes, over the positive half-line, with harmonic and power intensities. Corollaries to these universal convergence results yield the extreme-value statistics of Gumbel, Weibull, and Frechet.

Keywords: Random walks; Universal convergence; Poisson processes; Power statistics; Selfsimilar motions; Levy noises (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:512:y:2018:i:c:p:1160-1174

DOI: 10.1016/j.physa.2018.08.038

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