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

Li, Xiaoyue and Gray, Alison and Jiang, Daqing and Mao, Xuerong (2011) Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching. Journal of Mathematical Analysis and Applications, 376 (1). pp. 11-28. ISSN 0022-247X

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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.

    Item type: Article
    ID code: 29081
    Keywords: brownian motion, stochastic differential equation, generalized Itô's formula, markov chain, stochastic permanence, Probabilities. Mathematical statistics, Analysis, Applied Mathematics
    Subjects: Science > Mathematics > Probabilities. Mathematical statistics
    Department: Faculty of Science > Mathematics and Statistics
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    Depositing user: Pure Administrator
    Date Deposited: 07 Mar 2011 23:24
    Last modified: 04 Apr 2014 19:38
    URI: http://strathprints.strath.ac.uk/id/eprint/29081

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