论文标题
棕榈理论，随机措施和斯坦因耦合
Palm theory, random measures and Stein couplings
论文作者
论文摘要
我们建立了一种通用的浆果式类型，该类型在适当的力矩假设下在许多情况下具有最佳的界限。通过将一般结合与棕榈理论相结合，我们推断出一个新的误差，以评估正常近似与随机测量（包括随机几何形状）产生的统计数据的准确性。我们说明了在四个示例中使用绑定的使用：完全随机的度量，局部依赖随机过程的随机度量以及Ginibre-voronoi Tessellations的总边长度和Poisson-Voronoi Tessellations。此外，我们将一般界限应用于Stein耦合，并讨论占用问题中局部依赖和添加功能的特殊情况。
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.
