Instantaneous support propagation for [formula omitted]-Fleming–Viot processes

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.