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

Random walk on N with negative drift and absorption at 0, when conditioned on survival, has uncountably many invariant measures (quasistationary distributions, qsd ) νc. We study a Fleming-Viot(fv ) particle system driven by this process and show that mean normalized densities of the fv unique stationary measure converge to the minimal qsd , ν0, as N → ∞. Furthermore, every other qsd of the random walk (νc, c > 0) corresponds to a metastable state of the fv particle system.