Convergence of the EM method for NSDEs with time-dependent delay in the G-framework

Abstract

ABSTRACTConsider a neutral stochastic differential equation (NSDE) with time-dependent delay () in the G-framework where denotes a G-Brownian motion and the quadratic variation process of . We introduce an Euler–Maruyama (EM) method for solving this equation and prove that the EM approximate solution converges to the exact solution with a strong order of the mean square closeness equal to one under the global Lipschitz condition. A numerical example is provided to illustrate the effectiveness of our method.