Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains

Yong-Hua Mao () and Yan-Hong Song ()
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Yong-Hua Mao: Ministry of Education
Yan-Hong Song: Zhongnan University of Economics and Law

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1974-2008

Abstract: Abstract We present new criteria for geometric and algebraic transience for discrete-time transient Markov chains on general state spaces, based on the moment of the last exit time, the modified moment of the first return time and the drift condition for the transition kernel. These criteria turn out to be more convenient to use, supplementing and extending conditions introduced by Mao and Song [Stochastic Process. Appl. 124 (2014) 1648-1678]. Several applications are presented including discrete queueing Markov chains, Galton–Watson branching processes, downwardly skip-free chains, unrestricted random walks and autoregressive models of order one.

Keywords: Markov chain; Geometric transience; Algebraic transience; First return time; Last exit time; Drift condition; 60J05; 60J20; 60J35 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01105-5

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