Journal of the
Korean Mathematical Society JKMS

In this paper we consider functionals of the empirical age distribution of supercritical Bellman-Harris processes. Let $f: R^+ \ra R$ be a measurable function that integrates to zero with respect to the stable age distribution in a supercritical Bellman-Harris process with no extinction. We present sufficient conditions for the asymptotic normality of the mean of $f$ with respect to the empirical age distribution at time $t$.

Keywords: Bellman-Harris process, central limit theorems, empirical age distribution, stable age distribution

MSC numbers: 60J80, 60F05