NORMAL APPROXIMATION FOR COVERAGE MODELS OVER BINOMIAL POINT PROCESSES

• 成果类型: Article
• 署名作者: Goldstein, Larry; Penrose, Mathew D.
• 署名单位: University of Southern California; University of Bath
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP634
• 发表日期: 2010
• 页码: 696-721
• 关键词: CENTRAL LIMIT-THEOREMS

摘要

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.