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RIEB, Kobe University Site Map Access 日本語 Home Research & Education Publications RIEB Discussion Paper Series (English) RIEB Discussion Paper Series No.2017-02 RIEB Discussion Paper Series No.2017-02 Title Some Unified Results for Classical and Monotone Markov Chain Theory Abstract 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. Keywords Total variation, Markov chains, stochastic domination, coupling Inquiries Takashi KAMIHIGASHI Research Institute for Economics and Business Administration, Kobe University Rokkodai-cho, Nada-ku, Kobe 657-8501 Japan Phone: +81-78-803-7036 FAX: +81-78-803-7059 John STACHURSKI ANU College of Business and Economics, Australia About RIEB Faculty Seminars at RIEB Research & Education Sections Kobe University Site Policy Site Map Access Contact Us Copyright©1996-2018 Research Institute for Economics and Business Administration, Kobe University. All Rights Reserved.