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Article Dans Une Revue Electronic Journal of Probability Année : 2015

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

Résumé

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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Dates et versions

hal-00983773 , version 1 (25-04-2014)
hal-00983773 , version 2 (26-04-2014)
hal-00983773 , version 3 (28-01-2015)

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