Palm theory, random measures and Stein couplings

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