IDEAS home Printed from https://ideas.repec.org/p/kob/dpaper/dp2017-02.html
   My bibliography  Save this paper

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

    Download full text from publisher

    File URL: https://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2017-02.pdf
    File Function: First version, 2017
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shenghao Zhu, 2020. "Existence Of Stationary Equilibrium In An Incomplete‐Market Model With Endogenous Labor Supply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(3), pages 1115-1138, August.
    2. Mark Huggett, 2003. "When Are Comparative Dynamics Monotone?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(1), pages 1-11, January.
    3. S. Viswanathan & Adriano Rampini, 2013. "Household risk management," 2013 Meeting Papers 647, Society for Economic Dynamics.
    4. Takashi Kamihigashi & John Stachurski, 2014. "Stability Analysis for Random Dynamical Systems in Economics," Discussion Paper Series DP2014-35, Research Institute for Economics & Business Administration, Kobe University.
    5. Rampini, Adriano A. & Viswanathan, S., 2018. "Financing Insurance," CEPR Discussion Papers 12855, C.E.P.R. Discussion Papers.
    6. Bar Light, 2018. "Precautionary Saving in a Markovian Earnings Environment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 29, pages 138-147, July.
    7. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    8. Demange, Gabrielle & Laroque, Guy, 1998. "Long-sighted principal and myopic agents," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 119-146, September.
    9. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    10. Takashi Kamihigashi & John Stachurski, 2011. "Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2011-32, Research Institute for Economics & Business Administration, Kobe University.
    11. Chambers, Marcus J & Bailey, Roy E, 1996. "A Theory of Commodity Price Fluctuations," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 924-957, October.
    12. Nicola Pavoni & G. L. Violante, 2007. "Optimal Welfare-to-Work Programs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(1), pages 283-318.
    13. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    14. Marcet, Albert & Obiols-Homs, Francesc & Weil, Philippe, 2007. "Incomplete markets, labor supply and capital accumulation," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2621-2635, November.
    15. John Stachurski & Cuong Le Van, 2004. "Parametric continuity of stationary distributions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03331313, HAL.
    16. Karine Gobert & Michel Poitevin, 2006. "Non-commitment and savings in dynamic risk-sharing contracts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 357-372, June.
    17. Fenner, Trevor & Levene, Mark & Loizou, George, 2010. "Predicting the long tail of book sales: Unearthing the power-law exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2416-2421.
    18. Drewianka, Scott, 2006. "A generalized model of commitment," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 233-251, December.
    19. Michael Magill & Martine Quinzii, "undated". "Equity, Bonds, Growth And Inflation In A Quadratic Infinite Horizon Economy," Department of Economics 98-08, California Davis - Department of Economics.
    20. Marta González-Torrabadella & Josep Pijoan-Mas, 2006. "Flat tax reforms: a general equilibrium evaluation for Spain," Investigaciones Economicas, Fundación SEPI, vol. 30(2), pages 317-351, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kob:dpaper:dp2017-02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Office of Promoting Research Collaboration, Research Institute for Economics & Business Administration, Kobe University (email available below). General contact details of provider: https://edirc.repec.org/data/rikobjp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.