Limit Theorems for the Generalized Perimeters of Random Inscribed Polygons: II

被引：0
|
作者：
Simarova, E. N. [1 ,2 ]
机构：
[1] St Petersburg State Univ, St Petersburg 199034, Russia
[2] Euler Int Math Inst, St Petersburg 197022, Russia
来源：
VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS | 2021年 / 54卷 / 01期
关键词：
U-max-statistics; limit behavior; uniform distribution on circumference; generalized perimeter;
D O I：
10.1134/S1063454121010106
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：78 / 85
页数：8
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