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An Order-Theoretic Mixing Condition for Monotone Markov Chains

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  • Takashi Kamihigashi
  • John Stachurski

Abstract

We discuss stability of discrete-time Markov chains satisfying monotonicity and an order-theoretic mixing condition that can be seen as an alternative to irreducibility. A chain satisfying these conditions has at most one stationary distribution. Moreover, if there is a stationary distribution, then the chain is stable in an order-theoretic sense.

Suggested Citation

  • Takashi Kamihigashi & John Stachurski, 2011. "An Order-Theoretic Mixing Condition for Monotone Markov Chains," ANU Working Papers in Economics and Econometrics 2011-559, Australian National University, College of Business and Economics, School of Economics.
    • Handle: RePEc:acb:cbeeco:2011-559
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    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp559.pdf
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    References listed on IDEAS

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    1. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    2. 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.
    3. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521825658, June.
    4. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723, June.
    5. Takashi Kamihigashi & John Stachurski, 2009. "Asymptotics Of Stochastic Recursive Economies Under Monotonicity," KIER Working Papers 666, Kyoto University, Institute of Economic Research.
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    Cited by:

    1. Bayer, Christian & Rendall, Alan D. & Wälde, Klaus, 2019. "The invariant distribution of wealth and employment status in a small open economy with precautionary savings," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 17-37.
    2. , & ,, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    3. 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.
    4. Takashi Kamihigashi & John Stachurski, 2013. "Simple Fixed Point Results for Order-Preserving Self-Maps and Applications to Nonlinear Markov Operators," Discussion Paper Series DP2013-27, Research Institute for Economics & Business Administration, Kobe University.
    5. Kamihigashi, Takashi & Stachurski, John, 2016. "Seeking ergodicity in dynamic economies," Journal of Economic Theory, Elsevier, vol. 163(C), pages 900-924.
    6. repec:ipg:wpaper:2014-086 is not listed on IDEAS
    7. Takashi Kamihigashi & John Stachurski, 2014. "Interlinkage between Real Exchange rate and Current Account Behaviors: Evidence from India," Working Papers 2014-86, Department of Research, Ipag Business School.
    8. 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.
    9. Takashi Kamihigashi & John Stachurski, 2012. "Existence, Uniqueness and Stability of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2012-27, Research Institute for Economics & Business Administration, Kobe University.
    10. Takashi Kamihigashi & John Stachurski, 2011. "Stability of Stationary Distributions in Monotone Economies," ANU Working Papers in Economics and Econometrics 2011-561, Australian National University, College of Business and Economics, School of Economics.
    11. Takashi Kamihigashiw & John Stachurski, 2014. "Seeking Ergodicity in Dynamic Economies," Working Papers 2014-402, Department of Research, Ipag Business School.

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