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

Nicolas Champagnat (1, 2) , Denis Villemonais (1, 2)

1 IECL - Institut Élie Cartan de Lorraine
2 BIGS - Biology, genetics and statistics

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.

Mots clés: Fleming-Viot processes; Quasi-stationary distributions; Birth and death processes; Diffusion processes; Galton-Watson processes

Domaines: Probabilités [math.PR]

Nicolas Champagnat, Denis Villemonais. Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2021, 18, pp.1-15. ⟨10.30757/ALEA.v18-01⟩. ⟨hal-01895618⟩