Some results for the weak convergence of semi-implicit split-step methods.

In this paper, we obtain some results for the weak convergence of semi-implicit split-step (SISS)methods which are recently developed to solve a class of nonlinear stochastic differential equation with non-Lipschitz drift term. First, we present some moment estimates based on the actual and numerical solutions of stochastic Ginzburg-Landau equations by SISS methods. Then, we show that our theoretical results are consistent with the numerical results that are obtained by performing simulations. Finally, we present the weak convergence rate of SISS methods is approximately 1 with respect to the numerical results. [ABSTRACT FROM AUTHOR]