On weak implicit and predictor-corrector methods (Q1897658)

The paper provides a brief survey on weak schemes of discrete approximation for stochastic differential equations, i.e. the convergence order (w.r.t. the step size) of the expectation of the superposition of a smooth real function and the solution in the end point is considered. Using the stochastic Taylor expansion for obtaining approximation schemes of any order, the author gives an order 2 approximation scheme where no derivatives appear and where the Wiener integrals are substituted by easier random variables. Then order 2 implicit and predictor-corrector methods with these properties are given. At last, a systematic way is shown for obtaining higher-order implicit schemes by means of the stochastic Taylor expansion.