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

TL;DR

This paper studies the extinction behavior of Fleming-Viot particle systems with strong drift, showing conditions under which particles converge to zero in finite time, especially for Bessel processes and Brownian motion with strong drift.

Contribution

It provides new insights into the extinction criteria of Fleming-Viot systems with strong drift, extending understanding beyond classical Bessel process cases.

Findings

Particles with Bessel process motion and dimension less than 0 converge to zero in finite time.

Brownian motion with sufficiently strong drift also leads to finite-time extinction.

Extinction occurs regardless of the number of particles under strong drift conditions.

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.