An Analytic Approach to Fleming-Viot Processes with Interactive Selection

We study a class of (nonsymmetric) Dirichlet forms (E, D(E)) having a space of measures as state space E and derive some general results about them. We show that under certain conditions they generate diffusion processes M. In particular, if M is ergodic and (E, D(E)) is symmetric w.r.t. quasi-every starting point, the large deviations of the empirical distribution of M are governed by E. We apply all of this to construct Fleming-Viot processes with interactive selection and prove some results on their behavior. Among other things, we show some support properties for these processes using capacitary methods.