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On a Markov chain model for population growth subject to rare catastrophic events

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  • Huillet, Thierry E.

Abstract

We consider a Markov chain model for population growth subject to rare catastrophic events. In this model, the moves of the process are getting algebraically rare (as from x−λ) when the process visits large heights x, and given a move occurs and the height is large, the chain grows by one unit with large probability or undergoes a rare catastrophic event with small complementary probability ∼γ/x. We assume pure reflection at the origin. This chain is irreducible and aperiodic; it is always recurrent, either positive or null recurrent.

Suggested Citation

  • Huillet, Thierry E., 2011. "On a Markov chain model for population growth subject to rare catastrophic events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4073-4086.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4073-4086
    DOI: 10.1016/j.physa.2011.06.066
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    References listed on IDEAS

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    1. Eliazar, Iddo & Klafter, Joseph, 2006. "Growth-collapse and decay-surge evolutions, and geometric Langevin equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 106-128.
    2. Eliazar, Iddo & Klafter, Joseph, 2004. "A growth–collapse model: Lévy inflow, geometric crashes, and generalized Ornstein–Uhlenbeck dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 1-21.
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    Cited by:

    1. Guo, Bao & Li, Minglun & Zhou, Mengnan & Zhang, Fan & Wang, Pu, 2023. "A new anomalous travel demand prediction method combining Markov model and complex network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).

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