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Ultimate boundedness of impulsive stochastic delay differential equations with delayed impulses

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  • Liu, Zhiguang
  • Zhu, Quanxin

Abstract

This paper is devoted to studying the ultimate boundedness of impulsive stochastic delay differential equations (SDDEs) with delayed impulses. Using suitable Lyapunov functionals and Itoˆ’s formula, some necessary criteria are met to guarantee the system’s pth moment global exponential ultimate boundedness (p-MGEUB). The results show that the unbounded stochastic delay differential equation can be transformed into a bounded system by impulses. Moreover, our results generalize and improve some results in the literature. Finally, we provide an illustration to clarify our findings.

Suggested Citation

  • Liu, Zhiguang & Zhu, Quanxin, 2023. "Ultimate boundedness of impulsive stochastic delay differential equations with delayed impulses," Statistics & Probability Letters, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:stapro:v:199:y:2023:i:c:s0167715223000810
    DOI: 10.1016/j.spl.2023.109857
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    References listed on IDEAS

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    1. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    3. Hongyu Qin & Zhiyong Wang & Fumin Zhu & Jinming Wen, 2018. "Stability Analysis of Additive Runge-Kutta Methods for Delay-Integro-Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-5, June.
    4. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    5. Wang, Pengfei & Li, Shaoyu & Su, Huan, 2020. "Stabilization of complex-valued stochastic functional differential systems on networks via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    6. Fu, Xiaozheng & Zhu, Quanxin, 2020. "Exponential stability of neutral stochastic delay differential equation with delay-dependent impulses," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    7. Yong Tang & Lang Zhou & Jiahui Tang & Yue Rao & Hongguang Fan & Jihong Zhu, 2023. "Hybrid Impulsive Pinning Control for Mean Square Synchronization of Uncertain Multi-Link Complex Networks with Stochastic Characteristics and Hybrid Delays," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    8. Wei Hu, 2018. "A New Stability Criterion for Neutral Stochastic Delay Differential Equations with Markovian Switching," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, October.
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    Cited by:

    1. Yun Liu & Lifeng Guo & Xijuan Liu, 2023. "Dynamical Behaviors in a Stage-Structured Model with a Birth Pulse," Mathematics, MDPI, vol. 11(15), pages 1-13, July.

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