Estimation theory for continuous-time branching processes

Abstract

Results are given on estimation theory for some continuous-time branching processes assumed observed continuously in a fixed time interval [0, t]. Maximum likelihood theory works without problems for Markov branching processes. For Bellman-Harris (age-dependent) processes only the offspring distribution is easily estiamble. An "asymptotic Markovian property" of Bellman-Harris processes is observed. This property, which may have some independent interest, is then used as motivation for a study of a simple occurrence/exposure estimator for the Malthusian parameter. Some remarks are also given on previous results, in particular concerning cell growth studies.