On branching processes allowing immigration

Abstract

Continuous time one-type branching processes allowing immigration are considered. The invariant measure, which is shown to be unique, is exhibited. From this, a condition for positive recurrence similar to that of Heathcote's in the discrete time case is obtained. For the critical discrete time case, Seneta's sufficient condition for positive recurrence is improved to give a necessary and sufficient condition.

Identifiers

DOI

10.2307/3212633

Citations and references