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Stochastic stability of monotone economies in regenerative environments

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  • Foss, Sergey
  • Shneer, Vsevolod
  • Thomas, Jonathan P.
  • Worrall, Tim

Abstract

We introduce and analyze a new class of monotone stochastic recursions in a regenerative environment which is essentially broader than that of Markov chains. We prove stability theorems and apply our results to three canonical models in recursive economics, generalizing some known stability results to the cases when driving sequences are not independent and identically distributed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jetheo:v:173:y:2018:i:c:p:334-360
    DOI: 10.1016/j.jet.2017.11.004
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    Cited by:

    1. Bar Light, 2019. "General equilibrium in a heterogeneous-agent incomplete-market economy with many consumption goods and a risk-free bond," Papers 1906.06810, arXiv.org, revised Mar 2021.
    2. Thomas, Jonathan P. & Worrall, Tim, 2018. "Dynamic relational contracts under complete information," Journal of Economic Theory, Elsevier, vol. 175(C), pages 624-651.
    3. Fuh, Cheng-Der, 2021. "Asymptotic behavior for Markovian iterated function systems," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 186-211.
    4. Bar Light, 2021. "Stochastic Comparative Statics in Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 797-810, May.
    5. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    6. Onno Boxma & Andreas Löpker & Michel Mandjes & Zbigniew Palmowski, 2021. "A multiplicative version of the Lindley recursion," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 225-245, August.
    7. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org, revised Jan 2020.

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    More about this item

    Keywords

    Monotone economy; Stochastic recursion; Stochastic stability; One sector stochastic growth model; Bewley–Imrohoroglu–Huggett–Aiyagari model; Risk-sharing model;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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