The Transition Function of a Fleming-Viot Process

Abstract

Let $S$ be a compact metric space, let $\theta \geq 0$, and let $\nu_0$ be a Borel probability measure on $S$. An explicit formula is found for the transition function of the Fleming-Viot process with type space $S$ and mutation operator $(Af)(x) = (1/2)\theta\int_S(f(\xi) - f(x))\nu_0(d\xi)$.