On the central limit theorem for the stationary Poisson process of compact sets

被引：4

作者：

Pawlas, Z

Benes, V

机构：

[1] Charles Univ, Dept Probabil & Math Stat, Prague 18675 8, Czech Republic

[2] Acad Sci Czech Republ, Inst Informat Theory & Automat, CR-18208 Prague 8, Czech Republic

来源：

MATHEMATISCHE NACHRICHTEN | 2004年 / 267卷

关键词：

central limit theorem; Poisson point process; random measure; segment process; space of compact sets;

D O I：

10.1002/mana.200310154

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Stochastic geometry models based on a stationary Poisson point process of compact subsets of the Euclidean space are examined. Random measures on R-d, derived from these processes using Hausdorff and projection measures are studied. The central limit theorem is formulated in a way which enables comparison of the various estimators of the intensity of the produced random measures. Approximate confidence intervals for the intensity are constructed. Their use is demonstrated in an example of length intensity estimation for the segment processes. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：77 / 87

页数：11

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