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

Wiktorsson, Magnus LU (2001) In Annals of Applied Probability 11(2). p.470-487
Abstract
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

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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
numerical approximation, iterated Ito integral, multi-dimensional stochastic differential equation, variance mixture
in
Annals of Applied Probability
volume
11
issue
2
pages
470 - 487
publisher
Institute of Mathematical Statistics
external identifiers
  • scopus:0035538464
ISSN
1050-5164
DOI
10.1214/aoap/1015345301
language
English
LU publication?
yes
id
b2775156-fa48-4599-bb3e-0edef5c00644 (old id 1478488)
alternative location
http://www.jstor.org/stable/2667257
date added to LUP
2009-09-21 10:11:02
date last changed
2018-10-07 04:26:20
@article{b2775156-fa48-4599-bb3e-0edef5c00644,
  abstract     = {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/><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.},
  author       = {Wiktorsson, Magnus},
  issn         = {1050-5164},
  keyword      = {numerical approximation,iterated Ito integral,multi-dimensional stochastic differential equation,variance mixture},
  language     = {eng},
  number       = {2},
  pages        = {470--487},
  publisher    = {Institute of Mathematical Statistics},
  series       = {Annals of Applied Probability},
  title        = {Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions},
  url          = {http://dx.doi.org/10.1214/aoap/1015345301},
  volume       = {11},
  year         = {2001},
}