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

Liu, Yuanyuan; Zhang, Yuhui

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.

MARKOV processes; WIENER processes; CENTRAL limit theorem; LIMIT theorems; ERGODIC theory

Frontiers of Mathematics in China, 2015, Vol 10, Issue 4, p933

1673-3452

Academic Journal

10.1007/s11464-015-0488-5