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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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 376; no. 1; pp. 11 - 28
Main Authors: Li, Xiaoyue, Gray, Alison, Jiang, Daqing, Mao, Xuerong
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.04.2011
Elsevier
Subjects:
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
Online Access:Get full text
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.10.053