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Some Unified Results for Classical and Monotone Markov Chain Theory

Author

Listed:
  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • John Stachurski

    (ANU College of Business and Economics, Australia)

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.

Suggested Citation

  • Takashi Kamihigashi & John Stachurski, 2017. "Some Unified Results for Classical and Monotone Markov Chain Theory," Discussion Paper Series DP2017-02, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2017-02
    as

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    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2017-02.pdf
    File Function: First version, 2017
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    References listed on IDEAS

    as
    1. Chakraborty, Santanu & Rao, B. V., 1998. "Completeness of Bhattacharya metric on the space of probabilities," Statistics & Probability Letters, Elsevier, vol. 36(4), pages 321-326, January.
    2. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
    3. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    4. Schechtman, Jack, 1976. "An income fluctuation problem," Journal of Economic Theory, Elsevier, vol. 12(2), pages 218-241, April.
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