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.