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December 2012 Set reconstruction by Voronoi cells
M. Reitzner, E. Spodarev, D. Zaporozhets
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Adv. in Appl. Probab. 44(4): 938-953 (December 2012). DOI: 10.1239/aap/1354716584

Abstract

For a Borel set A and a homogeneous Poisson point process η in ∝d of intensity λ>0, define the Poisson--Voronoi approximation Aη of A as a union of all Voronoi cells with nuclei from η lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of E Vol(AΔ Aη) as λ→∞, where Vol is the Lebesgue measure. Estimates for all moments of Vol(Aη) and Vol(AΔ Aη) together with their asymptotics for large λ are obtained as well.

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M. Reitzner. E. Spodarev. D. Zaporozhets. "Set reconstruction by Voronoi cells." Adv. in Appl. Probab. 44 (4) 938 - 953, December 2012. https://doi.org/10.1239/aap/1354716584

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1280.60013
MathSciNet: MR3052844
Digital Object Identifier: 10.1239/aap/1354716584

Subjects:
Primary: 60D05
Secondary: 52A22, 60C05, 60G55

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 4 • December 2012
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