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Extinction behaviour for competing continuous-state population dynamics

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  • Xiong, Jie
  • Yang, Xu
  • Zhou, Xiaowen

Abstract

We consider a system of two stochastic differential equations (SDEs) with competing two-way interactions driven by Brownian motions and spectrally positive α-stable random measures. Such a SDE system can be identified as a Lotka-Volterra type population model. We find nearly sharp conditions for one of the population to become extinct or extinguished.

Suggested Citation

  • Xiong, Jie & Yang, Xu & Zhou, Xiaowen, 2026. "Extinction behaviour for competing continuous-state population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:spapps:v:196:y:2026:i:c:s0304414926000608
    DOI: 10.1016/j.spa.2026.104928
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    References listed on IDEAS

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    1. Ren, Yan-Xia & Xiong, Jie & Yang, Xu & Zhou, Xiaowen, 2022. "On the extinction-extinguishing dichotomy for a stochastic Lotka–Volterra type population dynamical system," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 50-90.
    2. Li, Pei-Sen, 2019. "A continuous-state polynomial branching process," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2941-2967.
    3. Xiong, Jie & Yang, Xu, 2019. "Existence and pathwise uniqueness to an SPDE driven by α-stable colored noise," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2681-2722.
    Full references (including those not matched with items on IDEAS)

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