On the transient behaviour of a Poisson branching process

Abstract

In general, information concerning the distribution of the time to absorption, T, of a simple branching (Galton-Watson) process for which extinction in finite mean time is certain, is difficult to obtain. The process of greatest biological interest is that for which the offspring distribution is Poisson, having p.g.f. F(s) = e^m(s-1), m < 1.