Generalized Fleming-Viot Processes with Mutations
Seminar Room 1, Newton Institute
We consider a generalized Fleming-Viot process with index $\alpha \in (1,2)$ with constant mutation rate $\theta>0$. We show that for any $\theta>0$, with probability one, there are no times at which there is a finite number of types in the population. This is different from the corresponding result of Schmuland for a classical Fleming-Viot process, where such times exist for $\theta$ sufficiently large. Along the proof we introduce a measure-valued branching process with non-Lipschitz interactive immigration which is of independent interest.