Instantaneous support propagation for $Λ$-Fleming-Viot processes

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 $S(ν* Z_t) \subseteq S(Z_t)$, 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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