A central limit theorem for the Poisson-Voronoi approximation

Autor(en): Schulte, Matthias
Stichwörter: Central limit theorem; Mathematics; Mathematics, Applied; Poisson point process; Poisson-Voronoi approximation; Random tessellation; Set reconstruction; Stochastic geometry; Wiener-Ito chaos expansion
Erscheinungsdatum: 2012
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: ADVANCES IN APPLIED MATHEMATICS
Volumen: 49
Ausgabe: 3-5
Startseite: 285
Seitenende: 306
Zusammenfassung: 
For a compact convex set K and a Poisson point process eta(lambda), the union of all Voronoi cells with a nucleus in K is the Poisson-Voronoi approximation of K. Lower and upper bounds for the variance and a central limit theorem for the volume of the Poisson-Voronoi approximation are shown. The proofs make use of the so-called Wiener-Ito chaos expansion and the central limit theorem is based on a more abstract central limit theorem for Poisson functionals, which is also derived. (C) 2012 Elsevier Inc. All rights reserved.
ISSN: 01968858
DOI: 10.1016/j.aam.2012.08.001

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