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

2021/01/19 by Federico Pianoforte, Pianoforte, Federico, Matthias Schulte +1
Mathematics · #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2101.07739

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 and point processes constructed using inradii and circumscribed radii of inhomogeneous Poisson-Voronoi tessellations.

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