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A Rate-Dependent Probabilistic Model of Hysteresis

Author

Listed:
  • Rod Cross

    (Department of Economics, Duncan Wing, Strathclyde Business School, 199 Cathedral Street, Glasgow G4 0QU, UK
    Deceased.
    These authors contributed equally to this work.)

  • Michael Grinfeld

    (Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK
    These authors contributed equally to this work.)

  • Harbir Lamba

    (Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
    These authors contributed equally to this work.)

Abstract

Instead of modelling an economic agent by a hysteron, we suggest a fluid–mechanical notion of rate-dependent hysteretic agents based on the theory of Poisson counters. It leads to a simple representation of assemblies of such agents. We discuss the properties of the new version of hysteresis and its advantages over classical models of hysteresis in economics.

Suggested Citation

  • Rod Cross & Michael Grinfeld & Harbir Lamba, 2024. "A Rate-Dependent Probabilistic Model of Hysteresis," Mathematics, MDPI, vol. 12(24), pages 1-8, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3924-:d:1542833
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    References listed on IDEAS

    as
    1. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    2. Scharfstein, David S & Stein, Jeremy C, 1990. "Herd Behavior and Investment," American Economic Review, American Economic Association, vol. 80(3), pages 465-479, June.
    3. Isaak D. Mayergoyz & Can E. Korman, 2021. "Economic Hysteresis and Its Mathematical Modeling," Papers 2107.10639, arXiv.org, revised Oct 2021.
    Full references (including those not matched with items on IDEAS)

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