Asymptotic properties of a human age distribution under a continuous net maternity function

Abstract

A useful and intuitively appealing proposition in theoretical demography asserts that the age distribution of a closed human populationis asymptotically independent of this shapein thedistant past, and is therefore exclusively determined by the historyof fertility and mortalitythat has prevailed during a reasonably long period of time. The mathematical foundations of this ergodic principle arelaid out in this article and thedetailsof its proofareworked out afteremphasizing an intuitive understanding of the process through which an age distribution tends to "forget" its past. The tendency for an unchanging schedule of vital ratesto produce a fixed agestructure in a closed population, is presented as a corollary of the main proposition dealt with in this article.