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A conditioned continuous-state branching process with applications

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  • Fang, Rongjuan
  • Li, Zenghu

Abstract

A supercritical CB-process conditioned on explosion is again a Markov process. We characterize the transition semigroup of the conditioned process by its Laplace transform and by a Doob’s h-transform. The conditioned CB-process is constructed as the strong solution of a stochastic integral equation. We use the distribution of the conditioned process to construct directly the canonical Kuznetsov measure of the CB-process. The later is reconstructed from positive paths picked up by a Poisson random measure based on the canonical Kuznetsov measure.

Suggested Citation

  • Fang, Rongjuan & Li, Zenghu, 2019. "A conditioned continuous-state branching process with applications," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 43-49.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:43-49
    DOI: 10.1016/j.spl.2019.04.013
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    References listed on IDEAS

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    1. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
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    Cited by:

    1. Hughes, Thomas & Zhou, Xiaowen, 2023. "Instantaneous support propagation for Λ-Fleming–Viot processes," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 535-560.
    2. 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.

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