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

2022/03/07 by Pianoforte, Federico, Schulte, Matthias
#Boolean model #Extremes #Inhomogeneous Poisson–Voronoi tessellation #Local dependence #Mathematik #Poisson process convergence #Stochastic geometry

paper · doi:10.15480/882.4198

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.

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