Absolutely continuous measure for a jump-type Fleming–Viot process

Abstract

In this paper, we prove that the random measure of the one-dimensional jump-type Fleming–Viot process is absolutely continuous with respect to the Lebesgue measure in R , provided the mutation operator satisfies certain regularity conditions. This result is an important step towards the representation of the Fleming–Viot process with jumps in terms of the solution of a stochastic partial differential equation.