IDEAS home Printed from https://ideas.repec.org/p/acb/cbeeco/2011-559.html
   My bibliography  Save this paper

An Order-Theoretic Mixing Condition for Monotone Markov Chains

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp559.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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, November.
    4. Bhattacharya,Rabi & Majumdar,Mukul, 2007. "Random Dynamical Systems," Cambridge Books, Cambridge University Press, number 9780521532723, November.
    5. Takashi Kamihigashi & John Stachurski, 2009. "Asymptotics Of Stochastic Recursive Economies Under Monotonicity," KIER Working Papers 666, Kyoto University, Institute of Economic Research.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Kamihigashi, Takashi & Stachurski, John, 2016. "Seeking ergodicity in dynamic economies," Journal of Economic Theory, Elsevier, vol. 163(C), pages 900-924.
    3. 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.
    4. , & ,, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    5. 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.
    6. 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.
    7. repec:ipg:wpaper:2014-086 is not listed on IDEAS
    8. 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.
    9. Takashi Kamihigashiw & John Stachurski, 2014. "Seeking Ergodicity in Dynamic Economies," Working Papers 2014-402, Department of Research, Ipag Business School.
    10. 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.
    11. 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.

    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. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    2. Foss, Sergey & Shneer, Vsevolod & Thomas, Jonathan P. & Worrall, Tim, 2018. "Stochastic stability of monotone economies in regenerative environments," Journal of Economic Theory, Elsevier, vol. 173(C), pages 334-360.
    3. Cai, Yiyong & Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic optimal growth with risky labor supply," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 167-176.
    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. Kiran Krishnamurthy, Chandra, 2012. "Optimal Management of Groundwater under Uncertainty: A Unified Approach," CERE Working Papers 2012:19, CERE - the Center for Environmental and Resource Economics, revised 30 Jun 2014.
    6. Fishman, Ram & B Krishnamurthy, Chandra Kiran, 2021. "An ecological golden rule," Resource and Energy Economics, Elsevier, vol. 64(C).
    7. Bishnu, Monisankar, 2010. "Essays on optimal allocation of resources by governments," ISU General Staff Papers 201001010800002441, Iowa State University, Department of Economics.
    8. Anna Jaśkiewicz & Andrzej S. Nowak, 2018. "On symmetric stochastic games of resource extraction with weakly continuous transitions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 239-256, July.
    9. Huang, Zaitang & Cao, Junfei, 2018. "Ergodicity and bifurcations for stochastic logistic equation with non-Gaussian Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 1-10.
    10. Mauro Gaggero & Giorgio Gnecco & Marcello Sanguineti, 2014. "Approximate dynamic programming for stochastic N-stage optimization with application to optimal consumption under uncertainty," Computational Optimization and Applications, Springer, vol. 58(1), pages 31-85, May.
    11. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    12. Makoto Yano & Yuichi Furukawa, 2021. "Two-Dimensional Constrained Chaos and Industrial Revolution Cycles with Mathemetical Appendices," KIER Working Papers 1057, Kyoto University, Institute of Economic Research.
    13. John Stachurski, 2019. "Firm Entry and Exit with Unbounded Productivity Growth," Papers 1910.14023, arXiv.org, revised Feb 2024.
    14. Colasante, Annarita & Palestrini, Antonio & Russo, Alberto & Gallegati, Mauro, 2017. "Adaptive expectations versus rational expectations: Evidence from the lab," International Journal of Forecasting, Elsevier, vol. 33(4), pages 988-1006.
    15. Çisem Bektur, 2013. "Performance of investment strategies in the absence of correct beliefs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(1), pages 23-37, May.
    16. Anna Jaśkiewicz & Andrzej Nowak, 2011. "Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics," Dynamic Games and Applications, Springer, vol. 1(2), pages 253-279, June.
    17. Chandra Kiran B. Krishnamurthy, 2017. "Optimal Management of Groundwater Under Uncertainty: A Unified Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(2), pages 351-377, June.
    18. Thomas, Jonathan P. & Worrall, Tim, 2018. "Dynamic relational contracts under complete information," Journal of Economic Theory, Elsevier, vol. 175(C), pages 624-651.
    19. Raphael L'evy & Marcin Pk{e}ski & Nicolas Vieille, 2022. "Stationary social learning in a changing environment," Papers 2201.02122, arXiv.org.
    20. Anna Jaśkiewicz & Janusz Matkowski & Andrzej Nowak, 2014. "On variable discounting in dynamic programming: applications to resource extraction and other economic models," Annals of Operations Research, Springer, vol. 220(1), pages 263-278, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:acb:cbeeco:2011-559. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/feanuau.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.