Minimal quasi-stationary distribution approximation for a birth and death process
Abstract
In a first part, we prove a Lyapunov-type criterion for the -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 . 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.
Keywords
Cite
@article{arxiv.1404.6648,
title = {Minimal quasi-stationary distribution approximation for a birth and death process},
author = {Denis Villemonais},
journal= {arXiv preprint arXiv:1404.6648},
year = {2015}
}
Comments
The new version provides an original Lyapunov-type criterion for the $\xi\_1$-positive recurrence of a birth and death process. An original result on the domain of attraction of the minimal quasi-stationary distribution of a birth and death processes is also included. (26 pages)