Asymptotic behavior of maximum likelihood estimators in a branching diffusion model

Abstract

In this paper the consistency and asymptotic normality of maximum-likelihood estimations for a super-critical branching diffusion model are obtained under certain conditions on its drift, variance and reproduction law. We proceeded by first studying the limit behavior of the Fisher information measure and related processes, and then verifying conditions established in Barndorff-Nielsen and Sorensen (Int stat Rev 62:133–165, 1994). This in turn uses the Martingale Law of Large Numbers as well as the Martingale Central Limit Theorem.