Convergence rate of EM scheme for \normalfont𝑆𝐷𝐷𝐸𝑠

Abstract

In this paper we investigate the convergence rate of the Euler-Maruyama (EM) scheme for a class of stochastic differential delay equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In particular, we reveal that the convergence rate of the Euler-Maruyama scheme is 1 2 \frac {1}{2} for the Brownian motion case, while we show that it is best to use the mean-square convergence for the pure-jump case and that the order of mean-square convergence is close to 1 2 \frac {1}{2} .