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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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.

Article information

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

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988374

Digital Object Identifier
doi:10.1214/aop/1176988374

Mathematical Reviews number (MathSciNet)
MR1330758

Zentralblatt MATH identifier
0833.60053

JSTOR
links.jstor.org

Subjects
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]

Keywords
Fleming-Viot processes Dirichlet forms exceptional sets

Citation

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. https://projecteuclid.org/euclid.aop/1176988374


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