Minimal quasi-stationary distribution approximation for a birth and death process

Denis Villemonais (1, 2, 3)

1 Probabilités et statistiques
2 TOSCA - TO Simulate and CAlibrate stochastic models
3 ENSMN - Ecole Nationale Supérieure des Mines de Nancy

We prove the ergodicity and the convergence of a Fleming-Viot type particle system to the minimal quasi-stationary distribution of some birth and death processes. Our main tool is a new tractable Lyapunov-type criterion which extends recent results on the domain of attraction of the minimal quasi-stationary distribution for birth and death processes.

Mots clés: Particle system; process with absorption; quasi-stationary distributions; birth and death processes

Domaines: Probabilités [math.PR]

Denis Villemonais. Minimal quasi-stationary distribution approximation for a birth and death process. 2014. ⟨hal-00983773v2⟩