Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching

In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of st...

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Vydáno v:	Journal of mathematical analysis and applications Ročník 376; číslo 1; s. 11 - 28
Hlavní autoři:	Li, Xiaoyue, Gray, Alison, Jiang, Daqing, Mao, Xuerong
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier Inc 01.04.2011 Elsevier
Témata:	Brownian motion Exact sciences and technology Generalized Itô's formula Markov chain Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Sciences and techniques of general use Stochastic differential equation Stochastic permanence Brownian motion Generalized Itô's formula Markov chain Stochastic permanence Stochastic differential equation Necessary condition Sufficient condition Mathematical analysis Probability distribution
ISSN:	0022-247X, 1096-0813
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Abstract	In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples.
AbstractList	In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples.
Author	Li, Xiaoyue Mao, Xuerong Jiang, Daqing Gray, Alison
Author_xml	– sequence: 1 givenname: Xiaoyue surname: Li fullname: Li, Xiaoyue email: lixy209@nenu.edu.cn, lixy209@yahoo.com.cn organization: School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, PR China – sequence: 2 givenname: Alison surname: Gray fullname: Gray, Alison organization: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, Scotland, UK – sequence: 3 givenname: Daqing surname: Jiang fullname: Jiang, Daqing organization: School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, PR China – sequence: 4 givenname: Xuerong surname: Mao fullname: Mao, Xuerong organization: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, Scotland, UK
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Snippet	In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or...
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SubjectTerms	Brownian motion Exact sciences and technology Generalized Itô's formula Markov chain Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Sciences and techniques of general use Stochastic differential equation Stochastic permanence
Title	Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching
URI	https://dx.doi.org/10.1016/j.jmaa.2010.10.053
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