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

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 RR, 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.