Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions
(2001) In Annals of Applied Probability 11(2). p.470487 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 tailsum distribution, which is a multivariate normal variance mixture, by a multivariate normal distribution.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1478488
 author
 Wiktorsson, Magnus ^{LU}
 organization
 publishing date
 2001
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 numerical approximation, iterated Ito integral, multidimensional 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
 10505164
 DOI
 10.1214/aoap/1015345301
 language
 English
 LU publication?
 yes
 id
 b2775156fa484599bb3e0edef5c00644 (old id 1478488)
 alternative location
 http://www.jstor.org/stable/2667257
 date added to LUP
 20160401 17:11:23
 date last changed
 20220205 21:24:16
@article{b2775156fa484599bb3e0edef5c00644, 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 tailsum distribution, which is a multivariate normal variance mixture, by a multivariate normal distribution.}}, author = {{Wiktorsson, Magnus}}, issn = {{10505164}}, keywords = {{numerical approximation; iterated Ito integral; multidimensional stochastic differential equation; variance mixture}}, language = {{eng}}, number = {{2}}, pages = {{470487}}, 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}}, doi = {{10.1214/aoap/1015345301}}, volume = {{11}}, year = {{2001}}, }