## Electronic Journal of Probability

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

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ejp/1465062333

Digital Object Identifier
doi:10.1214/EJP.v17-1770

Mathematical Reviews number (MathSciNet)
MR2878790

Zentralblatt MATH identifier
1258.60031

Subjects
Primary: 60G17: Sample path properties

Rights

#### Citation

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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