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.
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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. ⟨http://ejp.ejpecp.org/article/view/3482⟩. ⟨10.1214/EJP.v20-3482⟩. ⟨hal-00983773v3⟩

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