Normal approximation for coverage models over binomial point processes

L Goldstein, Mathew D Penrose

Research output: Contribution to journalArticle

12 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)696-721
Number of pages26
JournalAnnals of Applied Probability
Volume20
Issue number2
DOIs
Publication statusPublished - Apr 2010

Keywords

  • size biased coupling
  • Stochastic geometry
  • Berry-Esseen theorem
  • coverage process
  • Stein's method

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