The Poisson aggregation process

Iddo Eliazar

Chaos, Solitons & Fractals, 2016, vol. 83, issue C, 38-53

Abstract: In this paper we introduce and analyze the Poisson Aggregation Process (PAP): a stochastic model in which a random collection of random balls is stacked over a general metric space. The scattering of the balls’ centers follows a general Poisson process over the metric space, and the balls’ radii are independent and identically distributed random variables governed by a general distribution. For each point of the metric space, the PAP counts the number of balls that are stacked over it. The PAP model is a highly versatile spatial counterpart of the temporal M/G/∞ model in queueing theory. The surface of the moon, scarred by circular meteor-impact craters, exemplifies the PAP model in two dimensions: the PAP counts the number of meteor-impacts that any given moon-surface point sustained. A comprehensive analysis of the PAP is presented, and the closed-form results established include: general statistics, stationary statistics, short-range and long-range dependencies, a Central Limit Theorem, an Extreme Limit Theorem, and fractality.

Keywords: Poisson processes; M/G/∞ process; Short-range and long-range dependence; Central limit theorem; Extreme limit theorem (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:83:y:2016:i:c:p:38-53

DOI: 10.1016/j.chaos.2015.11.019

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