Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system

In general, population systems are often subject to environmental noise. This paper considers the stochastic functional Kolmogorov-type system d x ( t ) = diag ( x 1 ( t ) , … , x n ( t ) ) [ f ( x t ) d t + g ( x t ) d w ( t ) ] . Under the traditionally diagonally dominant condition, we study exis...

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Vydáno v:	Journal of mathematical analysis and applications Ročník 364; číslo 1; s. 104 - 118
Hlavní autoři:	Wu, Fuke, Hu, Shigeng, Liu, Yue
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier Inc 01.04.2010 Elsevier
Témata:	Exact sciences and technology Kolmogorov-type system Lotka–Volterra system Mathematical analysis Mathematics Moment average in time Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Sciences and techniques of general use Stochastic functional differential equations Stochastically ultimate boundedness Stochastically ultimate boundedness Kolmogorov-type system Stochastic functional differential equations Moment average in time Lotka–Volterra system Existence condition Asymptotic behavior Lotka-Volterra system Global solution Stochastic system Functional Mathematical analysis Positive solution Asymptotic solution Application
ISSN:	0022-247X, 1096-0813
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Abstract	In general, population systems are often subject to environmental noise. This paper considers the stochastic functional Kolmogorov-type system d x ( t ) = diag ( x 1 ( t ) , … , x n ( t ) ) [ f ( x t ) d t + g ( x t ) d w ( t ) ] . Under the traditionally diagonally dominant condition, we study existence and uniqueness of the global positive solution of this stochastic system, and its asymptotic bound properties and moment average boundedness in time. These properties are natural requirements from the biological point of view. As the special cases, we also discuss some stochastic Lotka–Volterra systems.
AbstractList	In general, population systems are often subject to environmental noise. This paper considers the stochastic functional Kolmogorov-type system d x ( t ) = diag ( x 1 ( t ) , … , x n ( t ) ) [ f ( x t ) d t + g ( x t ) d w ( t ) ] . Under the traditionally diagonally dominant condition, we study existence and uniqueness of the global positive solution of this stochastic system, and its asymptotic bound properties and moment average boundedness in time. These properties are natural requirements from the biological point of view. As the special cases, we also discuss some stochastic Lotka–Volterra systems.
Author	Wu, Fuke Hu, Shigeng Liu, Yue
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Keywords	Stochastically ultimate boundedness Kolmogorov-type system Stochastic functional differential equations Moment average in time Lotka–Volterra system Existence condition Asymptotic behavior Lotka-Volterra system Global solution Stochastic system Functional Mathematical analysis Positive solution Asymptotic solution Application
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SubjectTerms	Exact sciences and technology Kolmogorov-type system Lotka–Volterra system Mathematical analysis Mathematics Moment average in time Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Sciences and techniques of general use Stochastic functional differential equations Stochastically ultimate boundedness
Title	Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system
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