Central limit theorems for ergodic continuous-time Markov chains with applications to single birth processes

被引：13

作者：

Liu, Yuanyuan ^{[1
]}

Zhang, Yuhui ^{[2
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2015年 / 10卷 / 04期

关键词：

Markov process; single birth processes; central limit theorem (CLT); ergodicity; EXPONENTIAL ERGODICITY; POISSONS-EQUATION; CONVERGENCE; QUEUES; M/G/1;

D O I：

10.1007/s11464-015-0488-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain sufficient criteria for central limit theorems (CLTs) for ergodic continuous-time Markov chains (CTMCs). We apply the results to establish CLTs for continuous-time single birth processes. Moreover, we present an explicit expression of the time average variance constant for a single birth process whenever a CLT exists. Several examples are given to illustrate these results.

引用

页码：933 / 947

页数：15

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