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2021 Convergence of Markov chain transition probabilities
Michael Scheutzow, Dominik Schindler
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Electron. Commun. Probab. 26: 1-13 (2021). DOI: 10.1214/21-ECP395


Consider a discrete time Markov chain with rather general state space which has an invariant probability measure μ. There are several sufficient conditions in the literature which guarantee convergence of all or μ-almost all transition probabilities to μ in the total variation (TV) metric: irreducibility plus aperiodicity, equivalence properties of transition probabilities, or coupling properties. In this work, we review and improve some of these criteria in such a way that they become necessary and sufficient for TV convergence of all respectively μ-almost all transition probabilities. In addition, we discuss so-called generalized couplings.


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Michael Scheutzow. Dominik Schindler. "Convergence of Markov chain transition probabilities." Electron. Commun. Probab. 26 1 - 13, 2021.


Received: 21 December 2020; Accepted: 20 April 2021; Published: 2021
First available in Project Euclid: 12 May 2021

arXiv: 2004.10235
Digital Object Identifier: 10.1214/21-ECP395

Primary: 60J05
Secondary: 60G10

Keywords: convergence of transition probabilities , coupling , generalized coupling , Harris chain , invariant measure , irreducibility , Markov chain , Total variation


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