Maximum likelihood estimation for a branching diffusion process

Abstract

This paper investigates the properties of the maximum likelihood estimators of the drift and diffusion coefficients under three sampling schemes for a branching diffusion process in which the branching process is a linear birth process and the diffusion is in accordance with the Bro~cnian motion with drift.

Non‐parametric Estimation of the Death Rate in Branching Diffusions

“…However, statistical inference has not reached a unified form yet and only several particular cases of the general model of branching diffusions have been covered. To mention but a few: Adke (1983) studies the MLE theory in the specific case of a branching Brownian motion with no deaths, constant branching rate and reproduction mechanism which always creates k ¼ 2 offspring, for various sampling schemes of observation. Kulperger (1986) performs least-squares parametric estimation in branching diffusions with constant branching rate, constant diffusion coefficient and zero drift, but for a general offspring mechanism and including immigration.…”