Scaling Limit of the Fleming-Viot Multi-Colour Process

Abstract

We consider the $N$-particle Fleming-Viot process associated to a normally reflected diffusion with soft catalyst killing. The Fleming-Viot multi-colour process is obtained by attaching genetic information to the particles in the Fleming-Viot process. We establish that, after rescaling time by $t\mapsto Nt$, this genetic information converges to the (very different) Fleming-Viot process from population genetics, as $N\to \infty$. An extension is provided to dynamics given by Brownian motion with hard catalyst killing at the boundary of its domain.

44 pages. Final version of the paper. In the first version, we applied the main theorem to the dynamical historical processes and spine of the Fleming-Viot process. This has been removed, and will be turned into a sequel article

References in corpus (1)

• Slow and fast scales for superprocess limits of age-structured populations