Instantaneous support propagation for Λ-Fleming-Viot processes

2022/03/04 by Hughes, Thomas, Zhou, Xiaowen
#60G57 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2203.02415

Abstract

For a probability-measure-valued neutral Fleming-Viot process Z_t 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(Z_t) of the Fleming-Viot process satisfies S(ν* Z_t) ⊆ S(Z_t), 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 process.

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