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Instantaneous support propagation for Λ-Fleming–Viot processes

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  • Hughes, Thomas
  • Zhou, Xiaowen

Abstract

For a probability-measure-valued neutral Fleming–Viot process (Zt:t≥0) with Lévy mutation and resampling mechanism associated to a general Λ-coalescent with multiple collisions, we prove the instantaneous propagation of supports. That is, at any fixed time t>0, with probability one the closed support S(Zt) of the Fleming–Viot process satisfies S(ν∗Zt)⊆S(Zt), where ν is the Lévy measure of the mutation process. To show this result, we apply Donnelly–Kurtz’s lookdown particle representation for Fleming–Viot processes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:155:y:2023:i:c:p:535-560
    DOI: 10.1016/j.spa.2022.10.009
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    References listed on IDEAS

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    1. Fang, Rongjuan & Li, Zenghu, 2019. "A conditioned continuous-state branching process with applications," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 43-49.
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