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Published on: January 31, 2020
Sur les processus linéaires de naissance et de mort sous-critiques dans un environnement aléatoire
1Institut de Recherche pour le Développement, Unité 209 (UMMISCO), Bondy, France. nicolas.bacaer@ird.fr.
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.
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