RESEARCH ARTICLE

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

  • Yuanyuan LIU , 1 ,
  • Yuhui ZHANG 2
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  • 1. School of Mathematics and Statistics, New Campus, Central South University, Changsha 410083, China
  • 2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received date: 26 Jan 2015

Accepted date: 10 Apr 2015

Published date: 05 Jun 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

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.

Cite this article

Yuanyuan LIU , Yuhui ZHANG . Central limit theorems for ergodic continuous-time Markov chains with applications to single birth processes[J]. Frontiers of Mathematics in China, 2015 , 10(4) : 933 -947 . DOI: 10.1007/s11464-015-0488-5

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