Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4198
Publisher DOI: 10.1016/j.spa.2022.01.020
Title: Criteria for Poisson process convergence with applications to inhomogeneous Poisson–Voronoi tessellations
Language: English
Authors: Pianoforte, Federico 
Schulte, Matthias 
Keywords: Boolean model; Extremes; Inhomogeneous Poisson–Voronoi tessellation; Local dependence; Poisson process convergence; Stochastic geometry
Issue Date: 7-Feb-2022
Publisher: Elsevier
Source: Stochastic Processes and their Applications 147: 388-422 (2022-05-01)
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/11789
DOI: 10.15480/882.4198
ISSN: 0304-4149
Journal: Stochastic processes and their applications 
Institute: Mathematik E-10 
Document Type: Article
License: CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives) CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
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