Criteria for Poisson process convergence with applications to inhomogeneous Poisson–Voronoi tessellations

Federico Pianoforte and Matthias Schulte

Stochastic Processes and their Applications, 2022, vol. 147, issue C, 388-422

Abstract: This article employs the relation between probabilities of two consecutive values of a Poisson random variable to derive conditions for the weak convergence of point processes to a Poisson process. As applications, we consider the starting points of k-runs in a sequence of Bernoulli random variables, point processes constructed using inradii and circumscribed radii of inhomogeneous Poisson–Voronoi tessellations and large nearest neighbor distances in a Boolean model of disks.

Keywords: Poisson process convergence; Stochastic geometry; Inhomogeneous Poisson–Voronoi tessellation; Boolean model; Extremes; Local dependence (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.01.020

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