Normal approximation for coverage models over binomial point processes
Larry Goldstein and Mathew D. Penrose
Source: Ann. Appl. Probab. Volume 20, Number 2
(2010), 696-721.
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.
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Keywords: Stochastic geometry; coverage process; Berry–Esseen theorem; size biased coupling; Stein’s method
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aoap/1268143437
Digital Object Identifier: doi:10.1214/09-AAP634
Zentralblatt MATH identifier: 05704431
Mathematical Reviews number (MathSciNet): MR2650046
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