| Title | Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions |
| Authors | Magnus Wiktorsson |
| Alternative Location | http://www.jstor.org/stable..., Restricted Access |
| Alternative Location | http://dx.doi.org/10.1214/a... |
| Publication | The Annals of Applied Probability |
| Year | 2001 |
| Volume | 11 |
| Issue | 2 |
| Pages | 470 - 487 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Institute of Mathematical Statistics |
| Abstract English | We consider all two times iterated Ito 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<br> 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. |
| Keywords | numerical approximation, iterated Ito integral, multi-dimensional stochastic differential equation, variance mixture, |
| ISBN/ISSN/Other | ISSN: 10505164 |
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