On the simulation of iterated Ito integrals

We consider algorithms for simulation of iterated Ita integrals with applic ation to simulation of stochastic differential equations. The fact that the iterated Ito integral I-ij(t(n),t(n) + h) = integral (tn+h)(tn) integral (S)(tn) dW(i)(u)dW(j)(s) , conditioned on W-i(t(n) + h) - W-i(t(n)) and W-j(t(n) + h)- W-j(t(n)), has an infinitely divisible distribution utilised for the simultaneous simulati on of I-ij(t(n),t(n) + h), W-i(t(n) + h) - W-i(t(n)) and W-j(t(n) + h) - W- j(t(n)). Different simulation methods for the iterated fta integrals are in vestigated. We show mean-square convergence rates for approximations of sho t-noise type and asymptotic normality of the remainder of the approximation s. This together with the fact that the conditional distribution of I-ij(t( n), t(n) + h), apart from an additive constant, is a Gaussian variance mixt ure used to achieve an improved convergence rate. This is done by a couplin g method for the remainder of the approximation. (C) 2001 Elsevier Science B.V. All rights reserved. MSG: primary 60H05; secondary 60H10.