Normal approximation for coverage models over binomial point processes

Details Normal approximation for coverage models over binomial point processes Normal approximation for coverage models over binomial point processes

2008-12-16

arxiv.org/abs/0812.3084v3

Annals of Applied Probability 2010, Vol. 20, No. 2, 696-721

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP634 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP634

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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