RIEB, Kobe University

Some Unified Results for Classical and Monotone Markov Chain Theory

This paper expedites integration of two strands of the literature on stability of Markov chains: conventional, total variation based results and more recent order-theoretic results. First we introduce a complete metric on the set of 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.The conventional results can be recovered as a special case.