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Generalized Fleming-Viot Processes with Mutations

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Stochastic Partial Differential Equations (SPDEs)

We consider a generalized Fleming-Viot process with index $lpha in (1,2)$ with constant mutation rate $ heta>0$. We show that for any $ heta>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 $ heta$ sufficiently large. Along the proof we introduce a measure-valued branching process with non-Lipschitz interactive immigration which is of independent interest.

This talk is part of the Isaac Newton Institute Seminar Series series.

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