Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme

In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.

Automated summary

In this study, a new approximation scheme based on the explicit Milstein scheme is proposed for solving stochastic differential equations. Under sufficient conditions, the scheme is proven to have strong convergence and its stability is analyzed.