Abstract
We study a class of (nonsymmetric) Dirichlet forms $(\mathscr{E}, D(\mathscr{E}))$ 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 $\mathbf{M}$. In particular, if $\mathbf{M}$ is ergodic and $(\mathscr{E}, D(\mathscr{E}))$ is symmetric w.r.t. quasi-every starting point, the large deviations of the empirical distribution of $\mathbf{M}$ are governed by $\mathscr{E}$. 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.
Citation
Ludger Overbeck. Michael Rockner. Byron Schmuland. "An Analytic Approach to Fleming-Viot Processes with Interactive Selection." Ann. Probab. 23 (1) 1 - 36, January, 1995. https://doi.org/10.1214/aop/1176988374
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