Asymptotic behavior of maximum likelihood estimators in a branching diffusion model |
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| Authors: | Janko Hernandez Pablo Olivares Marcos Escobar |
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| Affiliation: | (1) Departamento Acadmico de Administracin Ro Hondo No.1 Col., Instituto Tecnologico Autnomo de Mexico (ITAM), Tizapn San Angel, Mexico City, DF, 01000, Mexico;(2) Department of Mathematics, Risklab, University of Toronto, 1 Spadina Crescent, Room 205, Toronto, Canada;(3) Department of Mathematics, Ryerson University, Toronto, Canada |
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| 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 Sørensen (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. |
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| Keywords: | Branching diffusion Fisher information Maximum likelihood estimators Semimartingales Ito’ s formula |
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