Delay-dependent Asymptotic Stability of Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion

Based on the classical probability, the stability of stochastic differential delay equations (SDDEs) whose coefficients are growing at most linearly has been investigated intensively. Moreover, the delay-dependent stability of highly nonlinear hybrid stochastic differential equations (SDEs) has also been studied recently. In this paper, using the nonlinear expectation theory, we first explore the delay-dependent criteria on the asymptotic stability for a class of highly nonlinear SDDEs driven by G-Brownian motion (G-SDDEs). Then, the (weak) quasi-sure stability of solutions to G-SDDEs is developed. Finally, an example is analyzed by the phi-max-mean algorithm to illustrate our theoretical results. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.