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

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  • Pianoforte, Federico
  • Schulte, Matthias

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.

Suggested Citation

  • Pianoforte, Federico & Schulte, Matthias, 2022. "Criteria for Poisson process convergence with applications to inhomogeneous Poisson–Voronoi tessellations," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 388-422.
    • Handle: RePEc:eee:spapps:v:147:y:2022:i:c:p:388-422
    DOI: 10.1016/j.spa.2022.01.020
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    References listed on IDEAS

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    1. Schuhmacher, Dominic, 2005. "Distance estimates for dependent superpositions of point processes," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1819-1837, November.
    2. repec:hal:journl:hal-02006796 is not listed on IDEAS
    3. Chenavier, Nicolas, 2014. "A general study of extremes of stationary tessellations with examples," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 2917-2953.
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