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

2014/04/26 by Denis Villemonais, Villemonais, Denis
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1404.6648

openalex publication_date 2014/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a first part, we prove a Lyapunov-type criterion for the ξ_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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