On monotonic convergence to stability

Abstract

The paper introduces, for age-distribution population vectors, a class of distances to the stable equivalent; each of these distances converges monotonically to zero as the population approaches stability. The Kullback distance, considered earlier to be unique as a measure with this property, turns out to be a mere specimen of this class. It is shown that the very feature of monotonic convergence agrees with demographic potential of age specific stabilization measures. The paper also introduces a class of monotonic measures of the convergence to each other of two non-stable populations with similar reproduction regimes. Numerical illustrations and demographic applications conclude the paper. © 2003 Max-Planck-Gesellschaft.