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Razumikhin-type theorem for neutral stochastic functional differential equations with unbounded delay

Wu, Fuke and Hu, Shigeng and Mao, Xuerong (2011) Razumikhin-type theorem for neutral stochastic functional differential equations with unbounded delay. Acta Mathematica Scientia, 31B (4). pp. 1245-1258.

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Abstract

This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.