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

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.

Key words： Markov process; single birth processes; central limit theorem (CLT); ergodicity

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