Abstract

Recently, W. Lao and M. Mayer (2008) developed U-max-statistics, where instead of averaging the values of the kernel over various subsets, the maximum of the kernel is considered. Such statistics often appear in stochastic geometry. This is the second part of the work devoted to the study of the generalized perimeter of a random inscribed polygon and the limit behavior of U-max-statistics related to it. Here we consider the case where the parameter arising in the definition of a generalized perimeter exceeds 1. The limit theorems in the case of a triangle are formulated and proved.

中文翻译：

---

随机内接多边形的广义周界的极限定理：II

摘要

最近，W。Lao和M. Mayer（2008）开发了U -max-statistics，其中考虑了内核的最大值，而不是对各个子集上的内核值取平均值。这种统计通常以随机几何形式出现。这是研究随机内接多边形的广义周长及其相关的U -max统计量极限行为的第二部分。在这里，我们考虑在广义周长的定义中出现的参数超过1的情况。制定并证明了三角形情况下的极限定理。