On the simulation of iterated Itô integrals
(2001) In Stochastic Processes and their Applications 91(1). p.151168 Abstract
 We consider algorithms for simulation of iterated Itô integrals with
application to simulation of stochastic differential equations. The
fact that the iterated Itô integral
I_{ij}(t_n,t_n+h)=\int_{t_n}^{t_n+h} \int_{t_n}^{s} dW_{i}(u)dW_{j}(s)
conditioned on W_i(t_n+h)W_i(t_n) and W_j(t_n+h)W_j(t_n), has an
infinitely divisible distribution is utilised for the simultaneous
simulation of $I_{ij}(t_n,t_n+h)$,W_{i}(t_n+h)W_{i}(t_n) and
W_j(t_n+h)W_j(t_n). Different simulation methods for the iterated
Itô integrals are investigated. We show mean square convergence rates
for approximations of shotnoise type and asymptotic normality of the
remainder of... (More)  We consider algorithms for simulation of iterated Itô integrals with
application to simulation of stochastic differential equations. The
fact that the iterated Itô integral
I_{ij}(t_n,t_n+h)=\int_{t_n}^{t_n+h} \int_{t_n}^{s} dW_{i}(u)dW_{j}(s)
conditioned on W_i(t_n+h)W_i(t_n) and W_j(t_n+h)W_j(t_n), has an
infinitely divisible distribution is utilised for the simultaneous
simulation of $I_{ij}(t_n,t_n+h)$,W_{i}(t_n+h)W_{i}(t_n) and
W_j(t_n+h)W_j(t_n). Different simulation methods for the iterated
Itô integrals are investigated. We show mean square convergence rates
for approximations of shotnoise type and asymptotic normality of the
remainder of the approximations. This together with the fact that the
conditional distribution of I_{ij}(t_n,t_n+h), apart from an additive
constant, is a Gaussian variance mixture is used to achieve an
improved convergence rate. This is done by a coupling method for the
remainder of the approximation. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1478506
 author
 Wiktorsson, Magnus ^{LU} and Rydén, Tobias ^{LU}
 organization
 publishing date
 2001
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Iterated Itô integral, Infinitely divisible distribution, Multidimensional stochastic differential equation, Numerical approximation, Class G distribution, Variance mixture, Coupling
 in
 Stochastic Processes and their Applications
 volume
 91
 issue
 1
 pages
 151  168
 publisher
 Elsevier
 external identifiers

 scopus:0007336796
 ISSN
 1879209X
 DOI
 language
 English
 LU publication?
 yes
 id
 b8cb22987ebe469698cfff1a298f15bc (old id 1478506)
 date added to LUP
 20090921 10:14:53
 date last changed
 20180610 04:40:29
@article{b8cb22987ebe469698cfff1a298f15bc, abstract = {We consider algorithms for simulation of iterated Itô integrals with<br/><br> application to simulation of stochastic differential equations. The<br/><br> fact that the iterated Itô integral<br/><br> I_{ij}(t_n,t_n+h)=\int_{t_n}^{t_n+h} \int_{t_n}^{s} dW_{i}(u)dW_{j}(s)<br/><br> conditioned on W_i(t_n+h)W_i(t_n) and W_j(t_n+h)W_j(t_n), has an<br/><br> infinitely divisible distribution is utilised for the simultaneous<br/><br> simulation of $I_{ij}(t_n,t_n+h)$,W_{i}(t_n+h)W_{i}(t_n) and<br/><br> W_j(t_n+h)W_j(t_n). Different simulation methods for the iterated<br/><br> Itô integrals are investigated. We show mean square convergence rates<br/><br> for approximations of shotnoise type and asymptotic normality of the<br/><br> remainder of the approximations. This together with the fact that the<br/><br> conditional distribution of I_{ij}(t_n,t_n+h), apart from an additive<br/><br> constant, is a Gaussian variance mixture is used to achieve an<br/><br> improved convergence rate. This is done by a coupling method for the<br/><br> remainder of the approximation.}, author = {Wiktorsson, Magnus and Rydén, Tobias}, issn = {1879209X}, keyword = {Iterated Itô integral,Infinitely divisible distribution,Multidimensional stochastic differential equation,Numerical approximation,Class G distribution,Variance mixture,Coupling}, language = {eng}, number = {1}, pages = {151168}, publisher = {Elsevier}, series = {Stochastic Processes and their Applications}, title = {On the simulation of iterated Itô integrals}, url = {http://dx.doi.org/}, volume = {91}, year = {2001}, }