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Practical stability of the analytical and numerical solutions of stochastic delay differential equations driven by G-Brownian motion via some novel techniques

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  • Yuan, Haiyan
  • Zhu, Quanxin

Abstract

In this paper, we focus on stochastic delay differential equations in the G-framework (G-SDDEs). We introduce the practical stability to examine whether the performance of G-SDDE near an unstable equilibrium point is acceptable. We establish a new generalized Gronwall inequality based on which we prove the practical mean-square (PMS) exponential stability of G-SDDE. We also establish the stability equivalence between the discrete and the continuous EM approximations for G-SDDE and then show that the continuous EM approximation can preserve the PMS exponential stability of G-SDDE. One numerical experiment is conducted to confirm our theoretical results.

Suggested Citation

  • Yuan, Haiyan & Zhu, Quanxin, 2024. "Practical stability of the analytical and numerical solutions of stochastic delay differential equations driven by G-Brownian motion via some novel techniques," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004727
    DOI: 10.1016/j.chaos.2024.114920
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    References listed on IDEAS

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    1. Yuan, Haiyan & Zhu, Quanxin, 2023. "Discrete-time feedback stabilization for neutral stochastic functional differential equations driven by G-Lévy process," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Eckhard Platen, 1999. "An Introduction to Numerical Methods for Stochastic Differential Equations," Research Paper Series 6, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Küchler, Uwe & Platen, Eckhard, 2000. "Strong discrete time approximation of stochastic differential equations with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 189-205.
    4. Ma, Li & Li, Yujing & Zhu, Quanxin, 2023. "Stability analysis for a class of stochastic delay nonlinear systems driven by G-Lévy Process," Statistics & Probability Letters, Elsevier, vol. 195(C).
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