Strong convergence of the split-step theta method for neutral stochastic delay differential equations

Neutral stochastic delay differential equations often appear in various fields of science and engineering. The aim of this article is to investigate the strong convergence of the split-step theta (SST) method for the neutral stochastic delay differential equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In particular, we reveal that the SST method with θ∈[0,1] strongly converges to the exact solution with the order 12. Some numerical results are presented to confirm the obtained results.