Least Squares Estimation for Discretely Observed Stochastic Lotka–Volterra Model Driven by Small α-Stable Noises

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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Main Authors: Chao Wei, Yan Wei, Yingying Zhou
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2020/8837689
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spelling doaj-bb2e0a1eefc449b7a122c656dc03e0b12020-11-25T04:11:34ZengHindawi LimitedDiscrete 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
collection DOAJ
language English
format Article
sources DOAJ
author Chao Wei
Yan Wei
Yingying Zhou
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
author_facet Chao Wei
Yan Wei
Yingying Zhou
author_sort Chao Wei
title 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_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_sort least squares estimation for discretely observed stochastic lotka–volterra model driven by small α-stable noises
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2020-01-01
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.
url http://dx.doi.org/10.1155/2020/8837689
work_keys_str_mv AT chaowei leastsquaresestimationfordiscretelyobservedstochasticlotkavolterramodeldrivenbysmallastablenoises
AT yanwei leastsquaresestimationfordiscretelyobservedstochasticlotkavolterramodeldrivenbysmallastablenoises
AT yingyingzhou leastsquaresestimationfordiscretelyobservedstochasticlotkavolterramodeldrivenbysmallastablenoises
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