Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching

Mao, Wei and Hu, Liangjian and Mao, Xuerong (2019) Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching. Electronic Journal of Qualitative Theory of Differential Equations, 52. pp. 1-17. ISSN 1417-3875

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    Abstract

    This paper focuses on the general decay stability of nonlinear neutral stochastic pantograph equations with Markovian switching (NSPEwMSs). Under the local Lipschitz condition and non-linear growth condition, the existence and almost sure stability with general decay of the solution for NSPEwMSs are investigated. By means of M-matrix theory, some sufficient conditions on the general decay stability are also established for NSPEwMSs.