Electronic Journal of Probability

Extinction of Fleming-Viot-type particle systems with strong drift

Mariusz Bieniek, Krzysztof Burdzy, and Soumik Pal

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We consider a Fleming-Viot-type particle system consisting of independently moving particles that are killed on the boundary of a domain. At the time of death of a particle, another particle branches. If there are only two particles and the underlying motion is a Bessel process on $(0,\infty)$, both particles converge to 0 at a finite time if and only if the dimension of the Bessel process is less than 0. If the underlying diffusion is Brownian motion with a drift stronger than (but arbitrarily close to, in a suitable sense) the drift of a Bessel process, all particles converge to 0 at a finite time, for any number of particles.

Article information

Electron. J. Probab., Volume 17 (2012), paper no. 11, 15 pp.

Accepted: 29 January 2012
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 60G17: Sample path properties

Fleming-Viot particle system extinction

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Bieniek, Mariusz; Burdzy, Krzysztof; Pal, Soumik. Extinction of Fleming-Viot-type particle systems with strong drift. Electron. J. Probab. 17 (2012), paper no. 11, 15 pp. doi:10.1214/EJP.v17-1770. https://projecteuclid.org/euclid.ejp/1465062333

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