Instantaneous support propagation for Λ-Fleming–Viot processes

Thomas Hughes and Xiaowen Zhou

Stochastic Processes and their Applications, 2023, vol. 155, issue C, 535-560

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.

Keywords: Fleming–Viot process; λ-coalescent; Lookdown representation; Support propagation; Lévy process (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2022.10.009

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