Palm theory, random measures and Stein couplings

Louis H. Y. Chen; Adrian Röllin; Aihua Xia

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arXiv · 2004.05026

Palm theory, random measures and Stein couplings

Louis H. Y. Chen·Adrian Röllin·Aihua Xia

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Abstract

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.

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Louis H. Y. Chen, Adrian Röllin, Aihua Xia. 2020-04-10. Palm theory, random measures and Stein couplings. https://arxiv.org/abs/2004.05026

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