On the simulation of iterated Itô integrals
(2001) In Stochastic Processes and their Applications 91(1). p.151-168- 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 shot-noise 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 shot-noise 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:
https://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, Multi-dimensional 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
- 1879-209X
- DOI
- 10.1016/S0304-4149(00)00053-3
- language
- English
- LU publication?
- yes
- id
- b8cb2298-7ebe-4696-98cf-ff1a298f15bc (old id 1478506)
- date added to LUP
- 2016-04-01 16:32:22
- date last changed
- 2022-02-05 08:53:50
@article{b8cb2298-7ebe-4696-98cf-ff1a298f15bc,
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 shot-noise 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 = {{1879-209X}},
keywords = {{Iterated Itô integral; Infinitely divisible distribution; Multi-dimensional stochastic differential equation; Numerical approximation; Class G distribution; Variance mixture; Coupling}},
language = {{eng}},
number = {{1}},
pages = {{151--168}},
publisher = {{Elsevier}},
series = {{Stochastic Processes and their Applications}},
title = {{On the simulation of iterated Itô integrals}},
url = {{http://dx.doi.org/10.1016/S0304-4149(00)00053-3}},
doi = {{10.1016/S0304-4149(00)00053-3}},
volume = {{91}},
year = {{2001}},
}