Given the solution (X_t) of a Stochastic Differential System, two situat,ions are considered: computat,ion of Ef(X_t) by a Monte-Carlo method and, in the ergodic case, integration of a function f w.r.t. the invariant probability law of (X_t) by simulating a simple t,rajectory.

For each case it is proved the expansion of the global approximat,ion error—for a class of discret,isat,ion schemes and of funct,ions f—in powers of the discretisation step size, extending in the fist case a result of Gragg for deterministic O.D.E.

Some nn~nerical examples are shown to illust,rate the applicat,ion of extrapolation methods, justified by the foregoing expansion, in order to improve the approximation accuracy