title: Sur les processus linéaires de naissance et de mort sous-critiques dans un environnement aléatoire.
abstract: An explicit formula is found for the rate of extinction of subcritical linear birth-and-death processes in a random environment. The formula is illustrated by numerical computations of the eigenvalue with largest real part of the truncated matrix for the master equation. The generating function of the corresponding eigenvector satisfies a Fuchsian system of singular differential equations. A particular attention is set on the case of two environments, which leads to Riemann's differential equation.
authors.affiliation: Institut de Recherche pour le Développement, Unité 209 (UMMISCO), Bondy, France. nicolas.bacaer@ird.fr.|Université Pierre et Marie Curie, Campus des Cordeliers, Paris, France. nicolas.bacaer@ird.fr.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Bacaër
mesh_terms: D004777:Environment; D008954:Models, Biological; D011157:Population Dynamics
keywords: Eigenvalue problem; Fuchsian differential equation; Quasi-birth-and-death process; Random environment