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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
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    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. 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.
    3. 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.
    4. 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.
    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)

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