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An Order-Theoretic Mixing Condition for Monotone Markov Chains

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  • Takashi Kamihigashi

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

  • John Stachurski

    (Research School of Economics, Australian National University, Canberra, Australia)

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.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2011-24.pdf
File Function: Revised version, 2011
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Bibliographic Info

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number DP2011-24.

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Length: 14 pages
Date of creation: Jul 2011
Date of revision: Sep 2011
Handle: RePEc:kob:dpaper:dp2011-24

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References

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  1. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521825658.
  2. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723.
  3. Takashi Kamihigashi & John Stachurski, 2009. "Asymptotics Of Stochastic Recursive Economies Under Monotonicity," KIER Working Papers 666, Kyoto University, Institute of Economic Research.
  4. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November.
  5. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
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Cited by:
  1. 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.
  2. Takashi Kamihigashi & John Stachurski, 2010. "Stochastic Stability in Monotone Economies," Discussion Paper Series DP2010-12, Research Institute for Economics & Business Administration, Kobe University.
  3. 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.
  4. Takashi Kamihigashi & John Stachurski, 2014. "Seeking Ergodicity in Dynamic Economies," Discussion Paper Series DP2014-22, Research Institute for Economics & Business Administration, Kobe University.
  5. 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.
  6. 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.

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