On error rates in normal approximations and simulation schemes for Levy processes
(2003) In Stochastic Models 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/302392
- author
- Signahl, Mikael LU
- organization
- publishing date
- 2003
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- divisible distributions, infinitely, normal approximation, edgeworth expansion, weak error rates
- in
- Stochastic Models
- 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
- 2016-04-01 16:12:39
- date last changed
- 2022-02-05 06:38:45
@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}}, keywords = {{divisible distributions; infinitely; normal approximation; edgeworth expansion; weak error rates}}, language = {{eng}}, number = {{3}}, pages = {{287--298}}, publisher = {{Taylor & Francis}}, series = {{Stochastic Models}}, title = {{On error rates in normal approximations and simulation schemes for Levy processes}}, url = {{http://dx.doi.org/10.1081/STM-120023562}}, doi = {{10.1081/STM-120023562}}, volume = {{19}}, year = {{2003}}, }