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A Note on the Stability of Monotone Markov Chains

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  • Bar Light

Abstract

This note studies monotone Markov chains, a subclass of Markov chains with extensive applications in operations research and economics. While the properties that ensure the global stability of these chains are well studied, their establishment often relies on the fulfillment of a certain splitting condition. We address the challenges of verifying the splitting condition by introducing simple, applicable conditions that ensure global stability. The simplicity of these conditions is demonstrated through various examples including autoregressive processes, portfolio allocation problems and resource allocation dynamics.

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  • Bar Light, 2024. "A Note on the Stability of Monotone Markov Chains," Papers 2401.11568, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2401.11568
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    1. John Kennan, 2001. "Uniqueness of Positive Fixed Points for Increasing Concave Functions on Rn: An Elementary Result," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(4), pages 893-899, October.
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