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

Xiaoyue Li, Alison Gray, Daqing Jiang, Xuerong Mao

Research output: Contribution to journalArticle

133 Citations (Scopus)
118 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)11-28
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume376
Issue number1
DOIs
Publication statusPublished - 1 Apr 2011

Fingerprint

Regime Switching
Permanence
Extinction
Markov processes
Logistics
Necessary Conditions
Sufficient Conditions
Markov chain
Probability distributions
Sample Path
Population Model
Stationary Distribution
Subsystem
Probability Distribution
Estimate

Keywords

  • brownian motion
  • stochastic differential equation
  • generalized Itô's formula
  • markov chain
  • stochastic permanence

Cite this

@article{097205a572d748649c86fc0896048c49,
title = "Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching",
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.",
keywords = "brownian motion, stochastic differential equation, generalized It{\^o}'s formula, markov chain, stochastic permanence",
author = "Xiaoyue Li and Alison Gray and Daqing Jiang and Xuerong Mao",
year = "2011",
month = "4",
day = "1",
doi = "10.1016/j.jmaa.2010.10.053",
language = "English",
volume = "376",
pages = "11--28",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
number = "1",

}

TY - JOUR

T1 - Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching

AU - Li, Xiaoyue

AU - Gray, Alison

AU - Jiang, Daqing

AU - Mao, Xuerong

PY - 2011/4/1

Y1 - 2011/4/1

N2 - 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.

AB - 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.

KW - brownian motion

KW - stochastic differential equation

KW - generalized Itô's formula

KW - markov chain

KW - stochastic permanence

UR - http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WK2-51BBM27-2&_user=875629&_coverDate=04%2F01%2F2011&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1625299499&_rerunOrigin=google&_acct=C000046979&_version=1&_urlVersion=0&_userid=875629&md5=272eee77d84b18289af55e9d8c517e2f&searchtype=a

U2 - 10.1016/j.jmaa.2010.10.053

DO - 10.1016/j.jmaa.2010.10.053

M3 - Article

VL - 376

SP - 11

EP - 28

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -