Stochastic demographic models: Age of a population
The developing age distribution in a sequence of population models is considered. For each integer N there is an initial population of size N with specified ages. At subsequent times the age distribution is obtained by the empirical measure of the ages, with each person having weight 1/N. Particles divide and die with rates which depend on the age of the particle and the age distribution in the population, and the process is Markov in the age distribution. The main theorem gives conditions for there to be a limiting measure valued process as N goes to infinity. The proofs use Hilbert space techniques, with the empirical measures being treated as elements in the dual of suitable Sobolev spaces.
scientific article; zbMATH DE number 4191456