IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i2p227-d318726.html
   My bibliography  Save this article

Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion

Author

Listed:
  • Lijun Pan

    (School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, China
    These authors contributed equally to this work.)

  • Jinde Cao

    (School of Mathematics, Southeast University, Nanjing 210096, China
    These authors contributed equally to this work.)

  • Yong Ren

    (School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, China
    These authors contributed equally to this work.)

Abstract

This paper is concerned with the p -th moment exponential stability and quasi sure exponential stability of impulsive stochastic functional differential systems driven by G-Brownian motion (IGSFDSs). By using G-Lyapunov method, several stability theorems of IGSFDSs are obtained. These new results are employed to impulsive stochastic delayed differential systems driven by G-motion (IGSDDEs). In addition, delay-dependent method is developed to investigate the stability of IGSDDSs by constructing the G-Lyapunov–Krasovkii functional. Finally, an example is given to demonstrate the effectiveness of the obtained results.

Suggested Citation

  • Lijun Pan & Jinde Cao & Yong Ren, 2020. "Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:227-:d:318726
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/2/227/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/2/227/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peng, Shiguo & Jia, Baoguo, 2010. "Some criteria on pth moment stability of impulsive stochastic functional differential equations," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1085-1092, July.
    2. Cheng, Pei & Deng, Feiqi, 2010. "Global exponential stability of impulsive stochastic functional differential systems," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1854-1862, December.
    3. Gao, Fuqing, 2009. "Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3356-3382, October.
    4. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kao, Yonggui & Zhu, Quanxin & Qi, Wenhai, 2015. "Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 795-804.
    2. Hu, Ying & Lin, Yiqing & Soumana Hima, Abdoulaye, 2018. "Quadratic backward stochastic differential equations driven by G-Brownian motion: Discrete solutions and approximation," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3724-3750.
    3. Peng Luo & Falei Wang, 2019. "Viability for Stochastic Differential Equations Driven by G-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(1), pages 395-416, March.
    4. Wang, Bingjun & Yuan, Mingxia, 2019. "Forward-backward stochastic differential equations driven by G-Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 39-47.
    5. Ting Cai & Pei Cheng, 2021. "Stability Analysis of Discrete-Time Stochastic Delay Systems with Impulses," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    6. Luo, Peng & Wang, Falei, 2015. "On the comparison theorem for multi-dimensional G-SDEs," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 38-44.
    7. Cheng, Pei & Deng, Feiqi, 2010. "Global exponential stability of impulsive stochastic functional differential systems," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1854-1862, December.
    8. Yao, Fengqi & Deng, Feiqi, 2012. "Exponential stability in terms of two measures of impulsive stochastic functional differential systems via comparison principle," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1151-1159.
    9. Li, Xinpeng & Peng, Shige, 2011. "Stopping times and related Itô's calculus with G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 121(7), pages 1492-1508, July.
    10. Zhang, Wei & Jiang, Long, 2021. "Solutions of BSDEs with a kind of non-Lipschitz coefficients driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 171(C).
    11. Cao, Wenping & Zhu, Quanxin, 2022. "Stability of stochastic nonlinear delay systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    12. Gao, Fuqing & Jiang, Hui, 2010. "Large deviations for stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2212-2240, November.
    13. Zhengqi Ma & Hongyin Jiang & Chun Li & Defei Zhang & Xiaoyou Liu, 2024. "Stochastic Intermittent Control with Uncertainty," Mathematics, MDPI, vol. 12(13), pages 1-15, June.
    14. Julian Holzermann, 2019. "Term Structure Modeling under Volatility Uncertainty," Papers 1904.02930, arXiv.org, revised Sep 2021.
    15. Zhou, Jianping & Park, Ju H. & Ma, Qian, 2016. "Non-fragile observer-based H∞ control for stochastic time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 69-83.
    16. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    17. Liu, Shuning & Lv, Guangying, 2024. "Almost sure polynomial stability and stabilization of stochastic differential systems with impulsive effects," Statistics & Probability Letters, Elsevier, vol. 206(C).
    18. 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.
    19. Li, Dingshi & Lin, Yusen, 2021. "Periodic measures of impulsive stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    20. Luo, Peng & Wang, Falei, 2014. "Stochastic differential equations driven by G-Brownian motion and ordinary differential equations," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3869-3885.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:227-:d:318726. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.