Fleming–Viot Particle System Driven by a Random Walk on $$\mathbb {N}$$

Abstract

A random walk on \({\mathbb N}\) with negative drift and absorption at 0, when conditioned on survival, has uncountably many invariant measures (quasi-stationary distributions, qsd ) \(\nu _c\). We study a Fleming–Viot (fv ) particle system driven by this process. Simulation results indicate that mean normalized densities of the fv unique stationary measure converge to the minimal qsd , \(\nu _0\), as \(N \rightarrow \infty \). Furthermore, every other qsd of the random walk (\(\nu _c\), \(c>0\)) corresponds to a metastable state of the fv particle system.