International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 515192, 20 pages
http://dx.doi.org/10.1155/2012/515192
Research Article

Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process

Pablo Olivares1 and Janko Hernandez2

1Department of Mathematics, Ryerson University, Toronto, ON, Canada M5B 2K3
2School of Business, ITAM, 01000 Mexico City, DF, Mexico

Received 29 June 2012; Accepted 18 October 2012

Academic Editor: Angelo Plastino

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.

Abstract

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.