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

Federico Pianoforte; Matthias Schulte

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arXiv · 2101.07739

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

Federico Pianoforte·Matthias Schulte

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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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Federico Pianoforte, Matthias Schulte. 2021-01-19. Criteria for Poisson process convergence with applications to inhomogeneous Poisson-Voronoi tessellations. https://arxiv.org/abs/2101.07739

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