Supercritical Age Dependent Branching Processes with Generation Dependence

Abstract

This paper examines the size, $Z(t)$, of a population as a function of time. $Z(t)$ is just like the ordinary Bellman-Harris age dependent branching process except that the number of daughters born to an individual in the $n$th generation is allowed to depend on $n$. The renewal theory of William Feller and Laplace transform theory are used to obtain the behavior of $EZ(t)$ as $t$ approaches infinity, and the convergence of $Z(t)/E(Z(t))$ in quadratic mean.