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Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Levy processes

Rubenthaler, S and Wiktorsson, Magnus LU (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.
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author
organization
publishing date
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
2007-09-20 18:58:10
date last changed
2018-01-07 09:14:43
@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},
  keyword      = {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},
  volume       = {108},
  year         = {2003},
}