Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises
Stochastic Lotka–Volterra model driven by small α-stable noises is used to describe population dynamics perturbed by random environment. However, parameters in the model are always unknown. The contrast function is given to obtain least squares estimators. The consistency and the rate of convergence...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/8837689 |
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| _version_ | 1832550930257543168 |
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| author | Chao Wei Yan Wei Yingying Zhou |
| author_facet | Chao Wei Yan Wei Yingying Zhou |
| author_sort | Chao Wei |
| collection | DOAJ |
| description | Stochastic Lotka–Volterra model driven by small α-stable noises is used to describe population dynamics perturbed by random environment. However, parameters in the model are always unknown. The contrast function is given to obtain least squares estimators. The consistency and the rate of convergence of the least squares estimators are proved, and the asymptotic distribution of the estimators are derived by Markov inequality, Cauchy–Schwarz inequality, and Gronwall’s inequality. Some numerical examples are provided to verify the effectiveness of the estimators. |
| format | Article |
| id | doaj-art-bb2e0a1eefc449b7a122c656dc03e0b1 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-bb2e0a1eefc449b7a122c656dc03e0b12025-02-03T06:05:28ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/88376898837689Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable NoisesChao Wei0Yan Wei1Yingying Zhou2School of Mathematics and Statistic, Anyang Normal University, Anyang 455000, ChinaSchool of Mathematics and Statistic, Anyang Normal University, Anyang 455000, ChinaSchool of Mathematics and Statistic, Anyang Normal University, Anyang 455000, ChinaStochastic Lotka–Volterra model driven by small α-stable noises is used to describe population dynamics perturbed by random environment. However, parameters in the model are always unknown. The contrast function is given to obtain least squares estimators. The consistency and the rate of convergence of the least squares estimators are proved, and the asymptotic distribution of the estimators are derived by Markov inequality, Cauchy–Schwarz inequality, and Gronwall’s inequality. Some numerical examples are provided to verify the effectiveness of the estimators.http://dx.doi.org/10.1155/2020/8837689 |
| spellingShingle | Chao Wei Yan Wei Yingying Zhou Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises Discrete Dynamics in Nature and Society |
| title | Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises |
| title_full | Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises |
| title_fullStr | Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises |
| title_full_unstemmed | Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises |
| title_short | Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises |
| title_sort | least squares estimation for discretely observed stochastic lotka volterra model driven by small α stable noises |
| url | http://dx.doi.org/10.1155/2020/8837689 |
| work_keys_str_mv | AT chaowei leastsquaresestimationfordiscretelyobservedstochasticlotkavolterramodeldrivenbysmallastablenoises AT yanwei leastsquaresestimationfordiscretelyobservedstochasticlotkavolterramodeldrivenbysmallastablenoises AT yingyingzhou leastsquaresestimationfordiscretelyobservedstochasticlotkavolterramodeldrivenbysmallastablenoises |