Tests for nonergodicity of denumerable continuous time Markov processes

We provide nonergodicity criteria for denumerable continuous time Markov processes in terms of test functions that satisfy Kaplan’s condition, which resolves an open problem given by [B.D. Choi, B. Kim, nonergodicity criteria for denumerable continuous time Markov processes, and Operations Research Letters 32 (2004) 575–580]. We give two examples where the nonergodicity criteria are used.