Random Generation of Stochastic Area Integrals

We describe a method of random generation of the integrals A 1;2 (t; t + h) = Z t+h t Z s t dw 1 (r)dw 2 (s) ? Z t+h t Z s t dw 2 (r)dw 1 (s) together with the increments w 1 (t+h)?w 1 (t) and w 2 (t+h)?w 2 (t) of a two-dimensional Brownian path (w 1 (t);w 2 (t)). The method chosen is based on Marsaglia's `rectangle-wedge-tail' method, gen-eralised to higher dimensions. The motivation is the need for a numerical scheme for simulation of strong solutions of general multi-dimensional stochastic diierential equations with an order of convergence O(h), where h is the step size. Previously no method has obtained an order of convergence better than O(p h) in the general case.