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On the Balance between Emigration and Immigration as Random Walks on Non-Negative Integers

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  • Thierry E. Huillet

    (Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS UMR-8089, 2 Avenue Adolphe-Chauvin, 95302 Cergy-Pontoise, France)

Abstract

Life is on a razor’s edge resulting from the random competitive forces of birth and death. We illustrate this aphorism in the context of three Markov chain population models where systematic random immigration events promoting growth are simultaneously balanced with random emigration ones provoking thinning. The origin of mass removals is either determined by external demands or by aging, leading to different conditions of stability.

Suggested Citation

  • Thierry E. Huillet, 2024. "On the Balance between Emigration and Immigration as Random Walks on Non-Negative Integers," Mathematics, MDPI, vol. 12(20), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3198-:d:1497380
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    References listed on IDEAS

    as
    1. Randall J. Swift, 2001. "Transient probabilities for a simple birth-death-immigration process under the influence of total catastrophes," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 25, pages 1-4, January.
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