Maximum likelihood estimation for stochastic Lotka–Volterra model with jumps
Abstract In this paper, we consider the stochastic Lotka–Volterra model with additive jump noises. We show some desired properties of the solution such as existence and uniqueness of positive strong solution, unique stationary distribution, and exponential ergodicity. After that, we investigate the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-04-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1605-z |
| _version_ | 1819108119694802944 |
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| author | Huiyan Zhao Chongqi Zhang Limin Wen |
| author_facet | Huiyan Zhao Chongqi Zhang Limin Wen |
| author_sort | Huiyan Zhao |
| collection | DOAJ |
| description | Abstract In this paper, we consider the stochastic Lotka–Volterra model with additive jump noises. We show some desired properties of the solution such as existence and uniqueness of positive strong solution, unique stationary distribution, and exponential ergodicity. After that, we investigate the maximum likelihood estimation for the drift coefficients based on continuous time observations. The likelihood function and explicit estimator are derived by using semimartingale theory. In addition, consistency and asymptotic normality of the estimator are proved. Finally, computer simulations are presented to illustrate our results. |
| first_indexed | 2024-12-22T03:04:52Z |
| format | Article |
| id | doaj.art-0718ec0241bc4c02890a49a22dd58bf2 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T03:04:52Z |
| publishDate | 2018-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-0718ec0241bc4c02890a49a22dd58bf22022-12-21T18:41:04ZengSpringerOpenAdvances in Difference Equations1687-18472018-04-012018112210.1186/s13662-018-1605-zMaximum likelihood estimation for stochastic Lotka–Volterra model with jumpsHuiyan Zhao0Chongqi Zhang1Limin Wen2School of Economics and Statistics, Guangzhou UniversitySchool of Economics and Statistics, Guangzhou UniversityDepartment of Statistics, Jiangxi Normal UniversityAbstract In this paper, we consider the stochastic Lotka–Volterra model with additive jump noises. We show some desired properties of the solution such as existence and uniqueness of positive strong solution, unique stationary distribution, and exponential ergodicity. After that, we investigate the maximum likelihood estimation for the drift coefficients based on continuous time observations. The likelihood function and explicit estimator are derived by using semimartingale theory. In addition, consistency and asymptotic normality of the estimator are proved. Finally, computer simulations are presented to illustrate our results.http://link.springer.com/article/10.1186/s13662-018-1605-zStochastic Lotka–Volterra modelSubordinatorMaximum likelihood estimationStationary distribution |
| spellingShingle | Huiyan Zhao Chongqi Zhang Limin Wen Maximum likelihood estimation for stochastic Lotka–Volterra model with jumps Advances in Difference Equations Stochastic Lotka–Volterra model Subordinator Maximum likelihood estimation Stationary distribution |
| title | Maximum likelihood estimation for stochastic Lotka–Volterra model with jumps |
| title_full | Maximum likelihood estimation for stochastic Lotka–Volterra model with jumps |
| title_fullStr | Maximum likelihood estimation for stochastic Lotka–Volterra model with jumps |
| title_full_unstemmed | Maximum likelihood estimation for stochastic Lotka–Volterra model with jumps |
| title_short | Maximum likelihood estimation for stochastic Lotka–Volterra model with jumps |
| title_sort | maximum likelihood estimation for stochastic lotka volterra model with jumps |
| topic | Stochastic Lotka–Volterra model Subordinator Maximum likelihood estimation Stationary distribution |
| url | http://link.springer.com/article/10.1186/s13662-018-1605-z |
| work_keys_str_mv | AT huiyanzhao maximumlikelihoodestimationforstochasticlotkavolterramodelwithjumps AT chongqizhang maximumlikelihoodestimationforstochasticlotkavolterramodelwithjumps AT liminwen maximumlikelihoodestimationforstochasticlotkavolterramodelwithjumps |