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首页> 外文期刊>Discrete and continuous dynamical systems >THE LASALLE-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY
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THE LASALLE-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

机译：具有无限时滞的中立型随机泛函微分方程的Laslate型定理

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The main aim of this paper is to establish the LaSalle-type theorem to locate limit sets for neutral stochastic functional differential equations with infinite delay, from which some criteria on attraction, boundedness and the almost sure stability with general decay rate and robustness are obtained. To make our theory more applicable, by the M-matrix theory, this paper also examines some conditions under which attraction and stability are guaranteed. These conditions also show that attraction and stability are robust with respect to stochastic perturbations. By specializing the general decay rate as the exponential decay rate and the polynomial decay rate, this paper examines two neutral stochastic integral-differential equations and shows that they are exponentially attractive and polynomially stable, respectively.
机译：本文的主要目的是建立LaSalle型定理，以定位具有无限时滞的中立随机泛函微分方程的极限集，从中获得一些关于吸引，有界以及几乎确定的稳定性以及一般衰减率和鲁棒性的准则。为了使我们的理论更适用，通过M矩阵理论，本文还研究了在某些条件下可以保证吸引力和稳定性。这些条件还表明，对于随机扰动，吸引力和稳定性很强。通过将一般衰减率专门化为指数衰减率和多项式衰减率，本文研究了两个中立随机积分微分方程，并证明它们分别是指数吸引的和多项式稳定的。

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