Stability equivalence for stochastic differential equations, stochastic differential delay equations and their corresponding Euler-Maruyama methods in G-framework

In this paper, we investigate the stability equivalence problem for stochastic differential delay equations, the auxiliary stochastic differential equations and their corresponding Euler-Maruyama (EM) methods under G-framework. More precisely, for p≥ 2, we prove the equivalence of practical exponential stability in p-th moment sense among stochastic differential delay equations driven by G-Brownian motion (G-SDDEs), the auxiliary stochastic differential equations driven by G-Brownian motion (G-SDEs), and their corresponding Euler-Maruyama methods, provided the delay or the step size is small enough. Thus, we can carry out careful simulations to examine the practical exponential stability of the underlying G-SDDE or G-SDE under some reasonable assumptions.