On Runge-Kutta-type methods for two-dimensional stochastic differential equations

In the multidimensional case, second-order weak Runge-Kutta methods for stochastic differential equation (SDE) need simulation of correlated random variables, unless the diffusion matrix of SDE satisfies the commutativity condition. In this paper, we show that this can be avoided for some types of diffusion matrices and test functions important for applications. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 403–412, July–September, 2006.