%0 Journal Article
%T Convergence of the EM method for NSDEs with time-dependent delay in the G-framework
%A Chunhui Mei
%A Shounian Deng
%A Yong Liang
%J Systems Science & Control Engineering
%D 2019
%R https://doi.org/10.1080/21642583.2019.1666320
%X Consider a neutral stochastic differential equation (NSDE) with time-dependent delay ¦Ä(t) ( 0¡Ü¦Ä(t)¡Ü¦Ó) in the G-framework d(x(t)£¿D(x(t£¿¦Ä(t))))=f(x(t),x(t£¿¦Ä(t)))dt+g(x(t),x(t£¿¦Ä(t)))dB(t)+h(x(t),x(t£¿¦Ä(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¨CMaruyama (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
%U https://www.tandfonline.com/doi/full/10.1080/21642583.2019.1666320