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

Consider a neutral stochastic differential equation (NSDE) with time-dependent delay δ(t) ( 0≤δ(t)≤τ) in the G-framework d(x(t)？D(x(t？δ(t))))=f(x(t),x(t？δ(t)))dt+g(x(t),x(t？δ(t)))dB(t)+h(x(t),x(t？δ(t)))d？B？(t), where B(t) denotes a G-Brownian motion and ？B？(t) the quadratic variation process of B(t). 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