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

Wei  Mao; Liangjian Hu; Xuerong Mao

doi:10.14232/ejqtde.2019.1.52

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

Wei Mao, Liangjian Hu, Xuerong Mao

Mathematics And Statistics

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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.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Electronic Journal of Qualitative Theory of Differential Equations
Volume	52
DOIs	https://doi.org/10.14232/ejqtde.2019.1.52
Publication status	Published - 5 Aug 2019

Keywords

neutral stochastic pantograph equations
Markovian switching
existence and uniqueness results
general decay stability

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Cite this

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title = "Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching",

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.",

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author = "Wei Mao and Liangjian Hu and Xuerong Mao",

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N2 - 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.

AB - 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.

KW - neutral stochastic pantograph equations

KW - Markovian switching

KW - existence and uniqueness results

KW - general decay stability

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