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May 2001 Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions
Magnus Wiktorsson
Ann. Appl. Probab. 11(2): 470-487 (May 2001). DOI: 10.1214/aoap/1015345301

Abstract

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.

Citation

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Magnus Wiktorsson. "Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions." Ann. Appl. Probab. 11 (2) 470 - 487, May 2001. https://doi.org/10.1214/aoap/1015345301

Information

Published: May 2001
First available in Project Euclid: 5 March 2002

zbMATH: 1019.60053
MathSciNet: MR1843055
Digital Object Identifier: 10.1214/aoap/1015345301

Subjects:
Primary: 60H05
Secondary: 60H10

Rights: Copyright © 2001 Institute of Mathematical Statistics

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Vol.11 • No. 2 • May 2001
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