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 | Enthalten in: | ADVANCES IN APPLIED MATHEMATICS | Band: | 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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