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On error rates in normal approximations and simulation schemes for Levy processes

Signahl, Mikael LU (2003) In Stochastic Models2001-01-01+01:00 19(3). p.287-298
Abstract
Let X = (X(t) : t greater than or equal to 0) be a Levy process. In simulation, one often wants to know at what size it is possible to truncate the small jumps while retaining enough accuracy. A useful tool here is the Edgeworth expansion. We provide a third order expansion together with a uniform error bound, assuming third Levy moment is 0. We next discuss approximating X in the finite variation case. Truncating the small jumps, we show that, adding their expected value, and further, including their variability by approximating by a Brownian motion, gives successively better results in general. Finally, some numerical illustrations involving a normal inverse Gaussian Levy process are given.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
divisible distributions, infinitely, normal approximation, edgeworth expansion, weak error rates
in
Stochastic Models2001-01-01+01:00
volume
19
issue
3
pages
287 - 298
publisher
Taylor & Francis
external identifiers
  • wos:000184929100001
  • scopus:0041917613
ISSN
1532-6349
DOI
10.1081/STM-120023562
language
English
LU publication?
yes
id
b810ed7e-2e00-4092-a399-d1d95a62e207 (old id 302392)
date added to LUP
2007-09-21 12:56:24
date last changed
2018-01-07 09:06:43
@article{b810ed7e-2e00-4092-a399-d1d95a62e207,
  abstract     = {Let X = (X(t) : t greater than or equal to 0) be a Levy process. In simulation, one often wants to know at what size it is possible to truncate the small jumps while retaining enough accuracy. A useful tool here is the Edgeworth expansion. We provide a third order expansion together with a uniform error bound, assuming third Levy moment is 0. We next discuss approximating X in the finite variation case. Truncating the small jumps, we show that, adding their expected value, and further, including their variability by approximating by a Brownian motion, gives successively better results in general. Finally, some numerical illustrations involving a normal inverse Gaussian Levy process are given.},
  author       = {Signahl, Mikael},
  issn         = {1532-6349},
  keyword      = {divisible distributions,infinitely,normal approximation,edgeworth expansion,weak error rates},
  language     = {eng},
  number       = {3},
  pages        = {287--298},
  publisher    = {Taylor & Francis},
  series       = {Stochastic Models2001-01-01+01:00},
  title        = {On error rates in normal approximations and simulation schemes for Levy processes},
  url          = {http://dx.doi.org/10.1081/STM-120023562},
  volume       = {19},
  year         = {2003},
}