Convergence and Stability of Split-Step Milstein Schemes for Stochastic Differential Equations

In this paper, the mean square convergence and stability of the split-step theta-Milstein schemes for stochastic differential equations are discussed. First, it is shown that these methods are mean square convergent with strong order 1. Then, we investigate the mean square stability of the split-step theta-Milstein methods. Finally, numerical examples are presented to illustrate the theoretical results.