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Stability Analysis for a Class of Stochastic Differential Equations with Impulses

Author

Listed:
  • Mingli Xia

    (School of Electric and Information Engineering, Zhongyuan University of Technology, Zhengzhou 450007, China)

  • Linna Liu

    (School of Electric and Information Engineering, Zhongyuan University of Technology, Zhengzhou 450007, China)

  • Jianyin Fang

    (School of Electric and Information Engineering, Zhongyuan University of Technology, Zhengzhou 450007, China)

  • Yicheng Zhang

    (School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China)

Abstract

This paper is concerned with the problem of asymptotic stability for a class of stochastic differential equations with impulsive effects. A sufficient criterion on asymptotic stability is derived for such impulsive stochastic differential equations via Lyapunov stability theory, bounded difference condition and martingale convergence theorem. The results show that the impulses can facilitate the stability of the stochastic differential equations when the original system is not stable. Finally, the feasibility of our results is confirmed by two numerical examples and their simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1541-:d:1104079
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    References listed on IDEAS

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    1. Cao, Wenping & Zhu, Quanxin, 2022. "Stability of stochastic nonlinear delay systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. 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.
    3. Bin Liu & Bo Xu & Guohua Zhang & Lisheng Tong, 2019. "Review of Some Control Theory Results on Uniform Stability of Impulsive Systems," Mathematics, MDPI, vol. 7(12), pages 1-28, December.
    4. Tadmon Calvin & Njike Tchaptchet Eric Rostand, 2022. "Impact of Financial Crisis on Economic Growth: A Stochastic Model," Stochastics and Quality Control, De Gruyter, vol. 37(1), pages 45-63, June.
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