Correction to a proposition related to ergodicity of Markov chains

Ziqi TAN; Xianping GUO

doi:10.1007/s11464-021-0929-2

Front. Math. China ›› 2021, Vol. 16 ›› Issue (3) : 801 -813. DOI: 10.1007/s11464-021-0929-2

RESEARCH ARTICLE

Correction to a proposition related to ergodicity of Markov chains

Ziqi TAN
, Xianping GUO ^†

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Abstract

Proposition 5.5.6 (ii) in the book Markov Chains and Stochastic Stability (2nd ed, Cambridge Univ. Press, 2009) has been used in the proof of a theorem about ergodicity of Markov chains. Unfortunately, an example in this paper shows that this proposition is not always true. Thus, a correction of this proposition is provided.

Keywords

Markov chain / split chain / petite set / minorization condition

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Ziqi TAN, Xianping GUO. Correction to a proposition related to ergodicity of Markov chains. Front. Math. China, 2021, 16(3): 801-813 DOI:10.1007/s11464-021-0929-2