Strong convergence of semi-implicit split-step methods for SDE with locally Lipschitz coefficients

We discuss mean-square strong convergence properties for numerical solutions of a class of stochastic differential equations with super-linear drift terms using semi-implicit split-step methods. Under a one-sided Lipschitz condition on the drift term and a global Lipschitz condition on the diffusion term, we show that these numerical procedures yield the usual strong convergence rate of 1/2. We also present simulation-based applications including stochastic logistic growth equations, and compare their empirical convergence with some alternate methods.