Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process
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...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/515192 |
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| _version_ | 1849305930546544640 |
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| author | Pablo Olivares Janko Hernandez |
| author_facet | Pablo Olivares Janko Hernandez |
| author_sort | Pablo Olivares |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2cf5a7234aeb4137aba36b68a8efb656 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2cf5a7234aeb4137aba36b68a8efb6562025-08-20T03:55:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/515192515192Maximum Likelihood Estimators for a Supercritical Branching Diffusion ProcessPablo Olivares0Janko Hernandez1Department of Mathematics, Ryerson University, Toronto, ON, M5B 2K3, CanadaSchool of Business, ITAM, 01000 Mexico City, DF, MexicoThe 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.http://dx.doi.org/10.1155/2012/515192 |
| spellingShingle | Pablo Olivares Janko Hernandez Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process International Journal of Mathematics and Mathematical Sciences |
| title | Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process |
| title_full | Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process |
| title_fullStr | Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process |
| title_full_unstemmed | Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process |
| title_short | Maximum Likelihood Estimators for a Supercritical Branching Diffusion Process |
| title_sort | maximum likelihood estimators for a supercritical branching diffusion process |
| url | http://dx.doi.org/10.1155/2012/515192 |
| work_keys_str_mv | AT pabloolivares maximumlikelihoodestimatorsforasupercriticalbranchingdiffusionprocess AT jankohernandez maximumlikelihoodestimatorsforasupercriticalbranchingdiffusionprocess |