Limit theorems for age-structured populations (Q922999)

A finite population of individuals is considered where each member is characterized by its age. The age-structure of the population at time t is the empirical distribution of the ages of the individuals present at time t. Each individual gives birth to a new individual (of age 0) with intensity \(\beta\) (a,\(\mu\)) and dies with intensity \(\gamma\) (a,\(\mu\)), where a is the age of the individual, \(\mu\) is the age-structure of the population, and \(\beta\) and \(\gamma\) are functions with certan regularity properties. Thus the age-structure is a weakly interacting stochastic process. The author proves a law of large numbers and a central limit theorem for the age-structure as the population size tends to infinity.