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

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.

Subjects

Boolean model

Extremes

Inhomogeneous Poisson–Voronoi tessellation

Local dependence

Poisson process convergence

Stochastic geometry

DDC Class

510: Mathematik

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publishedVersion

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https://creativecommons.org/licenses/by-nc-nd/4.0/

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1-s2.0-S0304414922000345-main.pdf

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1.67 MB

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