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Refracted continuous-state branching processes: Self-regulating populations

Author

Listed:
  • Murillo-Salas, A.
  • Pérez, J.L.
  • Siri-Jégousse, A.

Abstract

We construct a modified continuous-state branching process whose Malthusian parameter is replaced by another one when passing below a certain level. The construction is obtained via a Lamperti-like transform applied to a refracted Lévy process. Infinitesimal generator, probability of vanishing at infinity, of explosion and some path properties are also provided.

Suggested Citation

  • Murillo-Salas, A. & Pérez, J.L. & Siri-Jégousse, A., 2017. "Refracted continuous-state branching processes: Self-regulating populations," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 34-44.
    • Handle: RePEc:eee:stapro:v:123:y:2017:i:c:p:34-44
    DOI: 10.1016/j.spl.2016.11.026
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    References listed on IDEAS

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    1. Duhalde, Xan & Foucart, Clément & Ma, Chunhua, 2014. "On the hitting times of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4182-4201.
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