M. Wiktorsson, Joint characteristic function and simultaneous simulation of iterated Ito integrals for multiple independent Brownian motions, ANN APPL PR, 11(2), 2001, pp. 470-487
We consider all two-times iterated Ito integrals obtained by pairing nr ind
ependent standard Brownian motions, First we calculate the conditional join
t characteristic function of these integrals, given the Brownian increments
over the integration interval, and show that it has a form entirely simila
r to what is obtained in the univariate case. Then we propose an algorithm
for the simultaneous simulation of the m(2) integrals conditioned on the Br
ownian increments that achieves a mean square error of order 1/n(2), where
n is the number of terms in a truncated sum. The algorithm is based on appr
oximation of the tail-sum distribution, which is a multivariate normal vari
ance mixture, by a multivariate normal distribution.