Strong convergence of an explicit numerical approximation for n-dimensional superlinear SDEs with positive solutions

For a stochastic differential equation (SDE) with a unique positive solution, a rational numerical method is expected to be structure preserving. However, most existing methods are not, as far as we know. Some characteristics of the SDE models including the multi-dimension and super-linearity make it even more challenging. In this work, we fill the gap by proposing an explicit numerical method which is not only structure preserving but also cost effective. The strong convergence framework is set up by moment convergence analysis. We use the Lotka–Volterra system to elaborate our theory, nevertheless, the method works for a wide range of multi-dimensional superlinear SDE models.