Maximum likelihood estimation in branching process with continuous state space

Abstract

In some biological studies it is impossible to count the total number of individuals but the size of the population can be measured by its weight or volume. The numerical growth of such populations can be modelled by a branching process with state space [0, [infinity]). In this paper estimation of the mean of the offspring distribution of such a process is studied when the subordinator process is assumed to be the gamma process. The asymptotic properties of the estimator are established. It is also shown that the branching process with state space [0, [infinity]) when the corresponding subordinator process is a gamma process is a non-ergodic model and it belongs to the curved exponential family. The curvature of the model is also obtained.Curved exponential family gamma process non-ergodic model martingale limit theorem Toeplitz's lemma