Asymptotic Properties of Neutral Stochastic Functional Differential Equations with Infinite Delay

Rong Hu; De Jun Shao

doi:10.4028/www.scientific.net/AMM.235.119

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 235Asymptotic Properties of Neutral Stochastic...

Asymptotic Properties of Neutral Stochastic Functional Differential Equations with Infinite Delay

Abstract:

This paper considers the existence and uniqueness of solution to neutral stochastic functional differential equation with infinite delay with local Lipschitz condition but neither the linear growth condition. And we discuss the asymptotic properties of this solution including moment boundedness and the almost sure stability. The stability is more general and representative than the exponential stability. This investigation uses a specific Lyapunov function based on usual methods. To illustrate our idea more carefully, we introduce a function, which will be used as the decay function. A One-dimension nonlinear example is discussed to illustrate the theory.

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Periodical:

Applied Mechanics and Materials (Volume 235)

Pages:

119-123

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.235.119

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Online since:

November 2012

Authors:

Rong Hu, De Jun Shao

Keywords:

Asymptotic Properties, Infinite Delay, Lyapunov Function, Stochastic Functional Differential Equations

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