PIP: Classical demographic theory purports that the age structure of a population eventually stabilizes. Although the population may continue to grow, once equilibrium is reached, the proportions of people in different age categories do not change. Stochastic analogues can be proven if vital rates fluctuate according to a stationary stochastic process. The action of random matrix products on random vectors is studied. This permits the application of Hilbert's projective metric and leads to considerable simplification of the ergodic and central limit theory of population growth. Appropriate theorems and their proofs are presented.