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Stochastic Stability in Monotone Economies

Author

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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, Australia)

Abstract

This paper presents new order-theoretic conditions for global stability of monotone Markov processes with possibly non-compact state spaces. Our main result shows that a Markov process induced by a continuous and increasing transition law is globally stable if it admits a Lyapunovlike function, and becomes larger than any given element of the state space with positive probability, or smaller than any given element of the state space with positive probability. This result applies to a wide range of stochastic economic models.

Suggested Citation

  • Takashi Kamihigashi & John Stachurski, 2010. "Stochastic Stability in Monotone Economies," Discussion Paper Series DP2010-12, Research Institute for Economics & Business Administration, Kobe University.
    • Handle: RePEc:kob:dpaper:dp2010-12
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    More about this item

    Keywords

    Monotonicity; Stability; Markov process; Stochastic dynamics;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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