The Annals of Probability

An Analytic Approach to Fleming-Viot Processes with Interactive Selection

Ludger Overbeck, Michael Rockner, and Byron Schmuland

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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 information

Ann. Probab., Volume 23, Number 1 (1995), 1-36.

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


Primary: 60G57: Random measures
Secondary: 31C25: Dirichlet spaces 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 92O15 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Fleming-Viot processes Dirichlet forms exceptional sets


Overbeck, Ludger; Rockner, Michael; Schmuland, Byron. An Analytic Approach to Fleming-Viot Processes with Interactive Selection. Ann. Probab. 23 (1995), no. 1, 1--36. doi:10.1214/aop/1176988374.

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