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

Wei Mao, Liangjian Hu, Xuerong Mao

Research output: Contribution to journal › Article

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.
LanguageEnglish
Pages1-17
Number of pages17
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume52
DOIs
Publication statusPublished - 5 Aug 2019

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Almost Sure Stability
Pantograph Equation
Pantographs
Markovian Switching
Decay Rate
Stochastic Equations
Decay
Matrix Theory
Lipschitz condition
M-matrix
Growth Conditions
Sufficient Conditions

Keywords

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

Cite this

Mao, Wei ; Hu, Liangjian ; Mao, Xuerong. / Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching. In: Electronic Journal of Qualitative Theory of Differential Equations. 2019 ; Vol. 52. pp. 1-17.
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Mao, W, Hu, L & Mao, X 2019, 'Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching' Electronic Journal of Qualitative Theory of Differential Equations, vol. 52, pp. 1-17. https://doi.org/10.14232/ejqtde.2019.1.52

Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching. / Mao, Wei ; Hu, Liangjian; Mao, Xuerong.

In: Electronic Journal of Qualitative Theory of Differential Equations, Vol. 52, 05.08.2019, p. 1-17.

Research output: Contribution to journal › Article

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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.

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Mao W, Hu L, Mao X. Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching. Electronic Journal of Qualitative Theory of Differential Equations. 2019 Aug 5;52:1-17. https://doi.org/10.14232/ejqtde.2019.1.52

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