Inequalities for alternating branching processes

Abstract

A discrete time branching process is considered in which the offspring distribution alternates between two known probability distributions. There are two cases to consider, depending on which of the probability distributions initiates the process. It is shown, both graphically and analytically that for any pair of distributions, the probability of ultimate extinction is reduced if the process with the smaller individual probability of extinction starts first. An example is given in the case when the offspring distribution alternates between two geometric distributions.