The first- and last-birth problems for a multitype age-dependent branching process

Abstract

If B n is the time of the first birth in the n th generation in a supercritical irreducible multitype Crump–Mode process then when there are people in every generation B n /n converges to a constant; if D n is the time of the last birth in the n th generation then D n /n also converges to a constant on the survival set. Analogous results hold for the extreme members of the n th generation in a branching random walk.