The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations

This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under less restrictive conditions, the truncated Euler-Maruyama (TEM) schemes SDDEs are proposed, which numerical solutions bounded in q th moment ≥ 2 and converge to exact strongly any finite interval. The 1/2 order convergence rate is yielded. Furthermore, long-time asymptotic behaviors of solutions, such as stability mean square $\mathbb {P}-1$ , examined. Several experiments carried out illustrate our results.