On random sets connected to the partial records of Poisson point process

被引：4
|
作者：
Rivero, VM
机构：
[1] Univ Paris 06, CNRS, UMR 7599, Lab Probabil & Modeles Aleatoires, F-75252 Paris 05, France
[2] Univ Paris 07, F-75252 Paris 05, France
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2003年 / 16卷 / 01期
关键词：
Poisson point process; extremal process; regenerative sets; subordinators; fractal dimensions;
D O I：
10.1023/A:1022247025107
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Random intervals are constructed from partial records in a Poisson point process in] 0,infinity[x] 0,infinity[. These are used to cover partially [ 0,infinity[; the purpose of this work is to study the random set R that is left uncovered. We show that R enjoys the regenerative property and identify its distribution in terms of the characteristics of the Poisson point process. As an application we show that R is almost surely a fractal set and we calculate its dimension.
引用
收藏
页码：277 / 307
页数：31
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