  We derive the full kinetic equations describing the evolution of the
probability density distribution for a structured population such as cells
distributed according to their ages and sizes. The kinetic equations for such a
"sizer-timer" model incorporates both demographic and individual cell growth
rate stochasticities. Averages taken over the densities obeying the kinetic
equations can be used to generate a second order PDE that incorporates the
growth rate stochasticity. On the other hand, marginalizing over the densities
yields a modified birth-death process that shows how age and size influence
demographic stochasticity. Our kinetic framework is thus a more complete model
that subsumes both the deterministic PDE and birth-death master equation
representations for structured populations.
