Abstract
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.
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