The LaSalle-type theorem for neutral stochastic functional differential equations with infinite delay

Fuke Wu, Shigeng Hu

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17 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1065 - 1094
Number of pages30
JournalDiscrete and Continuous Dynamical Systems Series A
Issue number3
Publication statusPublished - 2012
Externally publishedYes

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