A unified stability theory for classical and monotone Markov chains

In this paper we integrate two strands of the literature on stability of general state Markov chains: conventional, total-variation-based results and more recent order-theoretic results. First we introduce a complete metric over Borel probability measures based on ‘partial’ stochastic dominance. We...

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Bibliographic Details
Published in:Journal of applied probability 2019-03, Vol.56 (1), p.1-22
Main Authors: Kamihigashi, Takashi, Stachurski, John
Format: Article
Language:English
Subjects:
Growth models
Markov analysis
Markov chains
Probability
Research Papers
Stability
Theory
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Summary:In this paper we integrate two strands of the literature on stability of general state Markov chains: conventional, total-variation-based results and more recent order-theoretic results. First we introduce a complete metric over Borel probability measures based on ‘partial’ stochastic dominance. We then show that many conventional results framed in the setting of total variation distance have natural generalizations to the partially ordered setting when this metric is adopted.
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2019.2