Copyright © 2012 Pablo Olivares and Janko Hernandez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The log-likelihood of a nonhomogeneous Branching Diffusion Process under several conditions assuring existence and uniqueness of the diffusion part and nonexplosion of the branching process. Expressions for different Fisher information measures are provided. Using the semimartingale structure of the process and its local characteristics, a Girsanov-type result is applied. Finally, an Ornstein-Uhlenbeck process with finite reproduction mean is studied. Simulation results are discussed showing consistency and asymptotic normality.