Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions
Wiktorsson, Magnus
Ann. Appl. Probab., Tome 11 (2001) no. 2, p. 470-487 / Harvested from Project Euclid
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We consider all two-times iterated Itô integrals obtained by pairing m independent standard Brownian motions. First we calculate the conditional joint characteristic function of these integrals, given the Brownian increments over the integration interval, and show that it has a form entirely similar 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 Brownian 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 approximation of the tail-sum distribution, which is a multivariate normal variance mixture, by a multivariate normal distribution.
Publié le : 2001-05-14
Classification:  Iterated Itô integral,  multidimensional stochastic differential equation,  numerical approximation,  variance mixture,  60H05,  60H10 
@article{1015345301,
     author = {Wiktorsson, Magnus},
     title = {Joint characteristic function and simultaneous simulation of
		 iterated It\^o integrals for multiple independent Brownian motions},
     journal = {Ann. Appl. Probab.},
     volume = {11},
     number = {2},
     year = {2001},
     pages = { 470-487},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1015345301}
}

Wiktorsson, Magnus. Joint characteristic function and simultaneous simulation of
		 iterated Itô integrals for multiple independent Brownian motions. Ann. Appl. Probab., Tome 11 (2001) no. 2, pp.  470-487. http://gdmltest.u-ga.fr/item/1015345301/