Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Levy processes
(2003) In Stochastic Processes and their Applications 108(1). p.1-26- Abstract
- We consider the Euler approximation of stochastic differential equations (SDEs) driven by Levy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y = Z(V) with V a subordinator and Z a stable process, we propose an approximation Y by Z(V-n) where V-n is an approximation of V. We then compute the rate of convergence for the approximation of the solution X of an SDE driven by Y using results about the stability of SDEs. (C) 2003 Elsevier B.V. All rights reserved.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/298570
- author
- Rubenthaler, S and Wiktorsson, Magnus LU
- organization
- publishing date
- 2003
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- rate, convergence, stochastic differential equation, numerical approximation, Levy process, shot noise representation, subordination
- in
- Stochastic Processes and their Applications
- volume
- 108
- issue
- 1
- pages
- 1 - 26
- publisher
- Elsevier
- external identifiers
-
- wos:000185803500001
- scopus:0141576699
- ISSN
- 1879-209X
- DOI
- 10.1016/S0304-4149(03)00100-5
- language
- English
- LU publication?
- yes
- id
- ddfcb3de-0f5c-4988-8122-80888cdb6f15 (old id 298570)
- date added to LUP
- 2016-04-01 16:23:28
- date last changed
- 2024-01-11 07:09:16
@article{ddfcb3de-0f5c-4988-8122-80888cdb6f15, abstract = {{We consider the Euler approximation of stochastic differential equations (SDEs) driven by Levy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y = Z(V) with V a subordinator and Z a stable process, we propose an approximation Y by Z(V-n) where V-n is an approximation of V. We then compute the rate of convergence for the approximation of the solution X of an SDE driven by Y using results about the stability of SDEs. (C) 2003 Elsevier B.V. All rights reserved.}}, author = {{Rubenthaler, S and Wiktorsson, Magnus}}, issn = {{1879-209X}}, keywords = {{rate; convergence; stochastic differential equation; numerical approximation; Levy process; shot noise representation; subordination}}, language = {{eng}}, number = {{1}}, pages = {{1--26}}, publisher = {{Elsevier}}, series = {{Stochastic Processes and their Applications}}, title = {{Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Levy processes}}, url = {{http://dx.doi.org/10.1016/S0304-4149(03)00100-5}}, doi = {{10.1016/S0304-4149(03)00100-5}}, volume = {{108}}, year = {{2003}}, }