We develop mathematical models describing the evolution of stochastic
age-structured populations. After reviewing existing approaches, we
formulate a complete kinetic framework for age-structured interacting
populations undergoing birth, death and fission processes in
spatially dependent environments. We define the full 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 behavior. Our approach utilizes mixed-type,
multidimensional probability distributions similar to those employed
in the study of gas kinetics and with terms that satisfy BBGKY-like
equation hierarchies.