PALM THEORY, RANDOM MEASURES AND STEIN COUPLINGS

• 成果类型: Article
• 署名作者: Chen, Louis H. Y.; Rollin, Adrian; Xia, Aihua
• 署名单位: National University of Singapore; National University of Singapore; University of Melbourne
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1666
• 发表日期: 2021
• 页码: 2881-2923
• 关键词: normal approximation; Voronoi tessellation; gaussian limits; statistics

摘要

We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of normal approximation to statistics arising from random measures, including stochastic geometry. We illustrate the use of the bound in four examples: completely random measures, excursion random measure of a locally dependent random process, and the total edge length of Ginibre-Voronoi tessellations and of Poisson-Voronoi tessellations. Moreover, we apply the general bound to Stein couplings and discuss the special cases of local dependence and additive functionals in occupancy problems.