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Razumikhin Theorems on Polynomial Stability of Neutral Stochastic Pantograph Differential Equations with Markovian Switching

Author

Listed:
  • Zihan Zou

    (School of Information and Mathematics, Yangtze University, Jingzhou 434023, China)

  • Yinfang Song

    (School of Information and Mathematics, Yangtze University, Jingzhou 434023, China)

  • Chi Zhao

    (School of Information and Mathematics, Yangtze University, Jingzhou 434023, China)

Abstract

This paper investigates the polynomial stability of neutral stochastic pantograph differential equations with Markovian switching (NSPDEsMS). Firstly, under the local Lipschitz condition and a more general nonlinear growth condition, the existence and uniqueness of the global solution to the addressed NSPDEsMS is considered. Secondly, by adopting the Razumikhin approach, one new criterion on the q th moment polynomial stability of NSPDEsMS is established. Moreover, combining with the Chebyshev inequality and the Borel–Cantelli lemma, the almost sure polynomial stability of NSPDEsMS is examined. The results derived in this paper generalize the previous relevant ones. Finally, two examples are provided to illustrate the effectiveness of the theoretical work.

Suggested Citation

  • Zihan Zou & Yinfang Song & Chi Zhao, 2022. "Razumikhin Theorems on Polynomial Stability of Neutral Stochastic Pantograph Differential Equations with Markovian Switching," Mathematics, MDPI, vol. 10(17), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3048-:d:896526
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    References listed on IDEAS

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    1. Wang, Junlan & Wang, Xin & Wang, Yantao & Zhang, Xian, 2021. "Non-reduced order method to global h-stability criteria for proportional delay high-order inertial neural networks," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    2. Mao, Xuerong, 1992. "Polynomial stability for perturbed stochastic differential equations with respect to semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 41(1), pages 101-116, May.
    3. Qi Wang & Huabin Chen & Chenggui Yuan, 2022. "A Note on Exponential Stability for Numerical Solution of Neutral Stochastic Functional Differential Equations," Mathematics, MDPI, vol. 10(6), pages 1-11, March.
    4. Mao, Xuerong, 1996. "Razumikhin-type theorems on exponential stability of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 233-250, December.
    5. Eftekhari, Tahereh & Rashidinia, Jalil, 2022. "A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise," Applied Mathematics and Computation, Elsevier, vol. 429(C).
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    Cited by:

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