Necessary conditions in limit theorems for cumulative processes

被引：18

作者：

Glynn, PW

Whitt, W

机构：

[1] AT&T Labs Res, Shannon Lab, Florham Pk, NJ 07932 USA

[2] Stanford Univ, Dept Management Sci & Engn, Stanford, CA 94305 USA

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2002年 / 98卷 / 02期

关键词：

central limit theorem; Markov chains; regenerative processes; cumulative processes; random sums; law of large numbers;

D O I：

10.1016/S0304-4149(01)00146-6

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：

We show that sufficient conditions in terms of moments for cumulative processes (additive functionals of regenerative processes) to satisfy the central limit theorem and the weak law of large numbers established in Glynn and Whitt (Stochastic Process. Appl. 47 (1993) 299-314) are also necessary, as previously conjectured. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：199 / 209

页数：11

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