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.
@article{1176988374,
author = {Overbeck, Ludger and Rockner, Michael and Schmuland, Byron},
title = {An Analytic Approach to Fleming-Viot Processes with Interactive Selection},
journal = {Ann. Probab.},
volume = {23},
number = {3},
year = {1995},
pages = { 1-36},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988374}
}
Overbeck, Ludger; Rockner, Michael; Schmuland, Byron. An Analytic Approach to Fleming-Viot Processes with Interactive Selection. Ann. Probab., Tome 23 (1995) no. 3, pp. 1-36. http://gdmltest.u-ga.fr/item/1176988374/