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

Denis Villemonais 1, 2
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : In a first part, we prove a Lyapunov-type criterion for the $\xi_1$-positive recurrence of absorbed birth and death processes and provide new results on the domain of attraction of the minimal quasi-stationary distribution. In a second part, we study the ergodicity and the convergence of a Fleming-Viot type particle system whose particles evolve independently as a birth and death process and jump on each others when they hit $0$. Our main result is that the sequence of empirical stationary distributions of the particle system converges to the minimal quasi-stationary distribution of the birth and death process.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [28 references]  Display  Hide  Download
Contributor : Denis Villemonais <>
Submitted on : Wednesday, January 28, 2015 - 5:40:01 PM
Last modification on : Friday, October 12, 2018 - 4:20:18 PM
Document(s) archivé(s) le : Wednesday, April 29, 2015 - 11:21:08 AM


Files produced by the author(s)


Distributed under a Creative Commons Attribution 4.0 International License



Denis Villemonais. Minimal quasi-stationary distribution approximation for a birth and death process. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2015, 20 (30), pp.1-18. ⟨⟩. ⟨10.1214/EJP.v20-3482⟩. ⟨hal-00983773v3⟩



Record views


Files downloads