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On stability of large-scale G-SDEs: A decomposition approach

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  • Yin, Wensheng
  • Cao, Jinde

Abstract

A decomposition approach is used to discuss the stability of large-scale stochastic differential equations driven by G-Brownian motion (G-SDEs, in short). This method establishes the connection between the large-scale G-SDEs and the corresponding reference G-SDEs (which is also called the isolated subsystems). It is shown that large-scale G-SDEs are exponentially stable in mean square if and only if each of the subsystems are exponentially stable in mean square. Finally, some interesting examples will be put forward to verifying the main results.

Suggested Citation

  • Yin, Wensheng & Cao, Jinde, 2021. "On stability of large-scale G-SDEs: A decomposition approach," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    • Handle: RePEc:eee:apmaco:v:388:y:2021:i:c:s0096300320304264
    DOI: 10.1016/j.amc.2020.125466
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    References listed on IDEAS

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    1. 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.
    2. Ren, Yong & He, Qian & Gu, Yuanfang & Sakthivel, R., 2018. "Mean-square stability of delayed stochastic neural networks with impulsive effects driven by G-Brownian motion," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 56-66.
    3. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
    4. Hu, Mingshang & Wang, Falei & Zheng, Guoqiang, 2016. "Quasi-continuous random variables and processes under the G-expectation framework," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2367-2387.
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