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Extinction of Fleming-Viot-type particle systems with strong drift. (English) Zbl 1258.60031
Summary: 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 a 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.

MSC:
60G17 Sample path properties
60J60 Diffusion processes
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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