Fractal Poisson processes

Iddo Eliazar and Joseph Klafter

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 21, 4985-4996

Abstract: The Central Limit Theorem (CLT) and Extreme Value Theory (EVT) study, respectively, the stochastic limit-laws of sums and maxima of sequences of independent and identically distributed (i.i.d.) random variables via an affine scaling scheme. In this research we study the stochastic limit-laws of populations of i.i.d. random variables via nonlinear scaling schemes. The stochastic population-limits obtained are fractal Poisson processes which are statistically self-similar with respect to the scaling scheme applied, and which are characterized by two elemental structures: (i) a universal power-law structure common to all limits, and independent of the scaling scheme applied; (ii) a specific structure contingent on the scaling scheme applied. The sum-projection and the maximum-projection of the population-limits obtained are generalizations of the classic CLT and EVT results — extending them from affine to general nonlinear scaling schemes.

Keywords: Fractal Poisson processes; Stochastic limit-laws; Nonlinear scaling; Power-laws; Self-similarity; Central Limit Theorem (CLT); Extreme Value Theory (EVT) (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:21:p:4985-4996

DOI: 10.1016/j.physa.2008.05.011

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