Abstract
•Satisfy uniform moment bounds for every moment.•Resemble similar stability properties of the actual solution (e.g. in terms of aymptotic Lyapunov stability).•Converge in the strong sense with the usual rate of ½.•Are more robust than other numerical methods with respect to changes in model parameters.
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.