Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions
(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:
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, 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
- 2016-04-01 17:11:23
- date last changed
- 2024-08-18 02:55:47
@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}}, keywords = {{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}}, doi = {{10.1214/aoap/1015345301}}, volume = {{11}}, year = {{2001}}, }