Joint characteristic function and simultaneous simulation of iterated Ito integrals for multiple independent Brownian motions

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.