Fleming-Viot particle system driven by a random walk on $\mathbb{N}$

Abstract

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 and show that mean normalized densities of the FV unique stationary measure converge to the minimal qsd, ${\nu }_0$, as $N\to \infty$. Furthermore, every other qsd of the random walk (${\nu }_c$, $c>0$) corresponds to a metastable state of the FV particle system.

17 pages, 10 figures

References in corpus (1)

• T. E. Harris' contributions to interacting particle systems and percolation

Cited by in corpus (2)

• A non-conservative Harris ergodic theorem
• Dynamics of a Fleming-Viot type particle system on the cycle graph