Transient features for Markovian binary trees

Abstract

We analyze a particular class of continuous-time multi-type branching processes, named Markovian binary trees (MBTs), and we focus on transient measures, such as the distribution of the population size at a finite time, the distribution of the time until extinction, and the distribution of the total family size until a given time, as well as the total size until extinction. Our results mainly are formulated as differential equations for probability generating functions and expressions for the factorial moments. They are applied to a demographic comparison of three countries.