Open Access
April 2010 Normal approximation for coverage models over binomial point processes
Larry Goldstein, Mathew D. Penrose
Ann. Appl. Probab. 20(2): 696-721 (April 2010). DOI: 10.1214/09-AAP634

Abstract

We give error bounds which demonstrate optimal rates of convergence in the CLT for the total covered volume and the number of isolated shapes, for germ-grain models with fixed grain radius over a binomial point process of n points in a toroidal spatial region of volume n. The proof is based on Stein’s method via size-biased couplings.

Citation

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Larry Goldstein. Mathew D. Penrose. "Normal approximation for coverage models over binomial point processes." Ann. Appl. Probab. 20 (2) 696 - 721, April 2010. https://doi.org/10.1214/09-AAP634

Information

Published: April 2010
First available in Project Euclid: 9 March 2010

zbMATH: 1200.60014
MathSciNet: MR2650046
Digital Object Identifier: 10.1214/09-AAP634

Subjects:
Primary: 60D05
Secondary: 05C80 , 60F05 , 62E17

Keywords: Berry–Esseen theorem , coverage process , size biased coupling , Stein’s method , Stochastic geometry

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.20 • No. 2 • April 2010
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