  We study mathematical models describing the evolution of stochastic
age-structured populations. After reviewing existing approaches, we present a
full kinetic framework for age-structured interacting populations undergoing
birth, death and fission processes, in spatially dependent environments. We
define the complete probability density for the population-size-age-chart and
find results under specific conditions. Connections with more classical models
are also explicitly derived. In particular, we show that factorial moments for
non-interacting processes are described by a natural generalization of the
McKendrick-von Foerster equation, which describes mean-field deterministic
behaviour. Our approach utilizes mixed type, multi-dimensional probability
distributions similar to those employed in the study of gas kinetics, with
terms that satisfy BBGKY-like equation hierarchies.
