Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution

TL;DR

This paper proves that the Fleming-Viot process converges to the minimal quasi-stationary distribution for certain Markov processes, with applications to birth-death, Galton-Watson, and diffusion processes.

Contribution

It establishes convergence conditions for the Fleming-Viot process to the minimal quasi-stationary distribution in non-compact spaces, extending previous results.

Findings

Fleming-Viot process converges to the minimal quasi-stationary distribution

Applicable to multi-dimensional birth-death and diffusion processes

Provides mild conditions for convergence in non-compact spaces

Abstract

We prove under mild conditions that the Fleming-Viot process selects the minimal quasi-stationary distribution for Markov processes with soft killing on non-compact state spaces. Our results are applied to multi-dimensional birth and death processes, continuous time Galton-Watson processes and diffusion processes with soft killing.