In this paper, we introduce the definitions of geometric strongly ergodic, strongly ergodic and weakly ergodic for continuous-state Markov chains, then we give a primary proof of equivalence of the ergodicities for continuous-state Markov chains.
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ZHANG Pengyan; YANG Weiguo. Primary Proof of Ergodicities for Continuous-State Markov Chains. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2018, 34(3): 312-318.