论文标题
高度非线性随机差延迟方程的延迟依赖性渐近稳定性由$ g $ -Brownian运动驱动
Delay-dependent Asymptotic Stability of Highly Nonlinear Stochastic Differential Delay Equations Driven by $G$-Brownian Motion
论文作者
论文摘要
基于经典概率，对其系数是线性或非线性但受线性函数界定的随机差延迟方程（SDDE）的稳定性标准已进行了深入研究。此外，最近研究了高度非线性混合随机微分方程的依赖稳定性。在本文中，通过使用非线性期望理论，我们探讨了由$ g $ -Brownian运动（$ G $ -SDDES）驱动的一类高度非线性混合随机差延迟方程的依赖稳定性。首先，我们给出了sublinear期望的初步。然后，提供了解决方案对$ g $ -sddes的延迟依赖性标准。最后，通过$φ$ -MAX-MAX-MEAN算法分析了一个说明性示例。
Based on the classical probability, the stability criteria for stochastic differential delay equations (SDDEs) where their coefficients are either linear or nonlinear but bounded by linear functions have been investigated intensively. Moreover, the dependent stability of the highly nonlinear hybrid stochastic differential equations is recently studied. In this paper, by using the nonlinear expectation theory, we explore the dependent stability of a class of highly nonlinear hybrid stochastic differential delay equations driven by $G$-Brownian motion ($G$-SDDEs). Firstly, we give preliminaries of sublinear expectation. Then, the delay-dependent criteria of the stability and boundedness of solutions to $G$-SDDEs is provided. Finally, an illustrative example is analyzed by the $φ$-max-mean algorithm.
