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A unified stability theory for classical and monotone Markov chains

  • Takashi Kamihigashi (a1) and John Stachurski (a2)

Abstract

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.

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Corresponding author

*Postal address: Research Institute of Economics and Business, Kobe University, Japan. Email address: tkamihig@rieb.kobe-u.ac.jp
**Postal address: Research School of Economics, Australian National University, Australia. Email address: john.stachurski@anu.edu.au

References

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