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

Haiyan Yuan and Quanxin Zhu

Chaos, Solitons & Fractals, 2024, vol. 183, issue C

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.

Keywords: G-Brownian motion; Stochastic delay differential equation; Euler–Maruyama method; PMS exponential stability (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004727

DOI: 10.1016/j.chaos.2024.114920

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