Divergence rates for the number of rare numbers

被引：5

作者：

Key, ES

机构：

[1] Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee

来源：

JOURNAL OF THEORETICAL PROBABILITY | 1996年 / 9卷 / 02期

关键词：

rare numbers; almost sure convergence; subadditive;

D O I：

10.1007/BF02214657

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：

Suppose that X(1),X(2),... is a sequence of i.i.d. random variables taking value in Z(+). Consider the random sequence A(X) = (X(1),X(2),...). Let Y-n be the number of integers which appear exactly once in the first n terms of A(X). We investigate the limit behavior of Y-n/E[Y-n] and establish conditions under which we have almost sure convergence to 1. We also find conditions under which we determine the rate of growth of E[Y-n]. These results extend earlier work by the author.

引用

页码：413 / 428

页数：16