RANDOM GENERATION OF STOCHASTIC AREA INTEGRALS

The authors describe a method of random generation of the integrals A1 ,2(t,t+h) = integral-t+h/t integral-s/t dw1(r)dw2(s) - integral-t+h/t integral-s/t dw2(r)dw1(s), together with the increments w1(t+h) - w1(t ) and w2(t+h) - w2(t) of a two-dimensional Brownian path (w1(t), w2(t) ). The method chosen is based on Marsaglia's ''rectangle-wedge-tail'' method, generalised to higher dimensions. The motivation is the need f or a numerical scheme for simulation of strong solutions of general mu ltidimensional stochastic differential equations with an order of conv ergence O(h), where h is the stepsize. Previously, no method has obtai ned an order of convergence better than O(square-root h) in the genera l case.