A step size control algorithm for the weak approximation of stochastic differential equations

A vriable step size control algorithm for the weak approximation of stochastic differential equations is introduced. The algorithm is based on embedded Runge-Kutta methods which yield two approximations of different orders with a negligible additional computational effort. The difference of these two approximations is used as an estimator for the local error of the less precise approximation. Some numerical results are presented to illustrate the effectiveness of the introduced step size control method.