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.

中文翻译：

---

人口稳定稳定增长。

古典人口理论声称人口的年龄结构最终会稳定下来。尽管人口可能继续增长，但一旦达到平衡，不同年龄类别的人口比例就不会改变。如果生命率根据固定的随机过程而波动，则可以证明是随机类似物。研究了随机矩阵乘积对随机向量的作用。这允许应用希尔伯特的投影度量，并导致人口增长的遍历遍历和中心极限理论大大简化。给出了适当的定理及其证明。