Asymptotically optimum quadrature formulae for stochastic integrals

Quadrature formulae are given for the calculation of stochastic integrals of the form ??f0 1(t,Wt)dt and ??g0 1(t,Wt) ?? dWt, based on measurements of a Brownian motion Wt taken at points of a regular partition. For the first a trapezoidal rule suffices; for the second a five-point formula is required. The approximation sequences these formulae generate have asymptotically optimum properties for almost every path of Wt.