The Library
Exact simulation of the extrema of stable processes
Tools
González Cázares, Jorge Ignacio, Mijatović, Aleksandar and Uribo Bravo, Gerónimo (2019) Exact simulation of the extrema of stable processes. Advances in Applied Probability, 51 (4). pp. 967-993. doi:10.1017/apr.2019.39 ISSN 0001-8678.
|
PDF
WRAP-exact-simulation-extrema-stable-processes-Mijatovic-2019.pdf - Accepted Version - Requires a PDF viewer. Download (994Kb) | Preview |
Official URL: https://doi.org/10.1017/apr.2019.39
Abstract
We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the fast (DCFTP). We establish a novel perpetuity equation for the supremum (via the representation of the concave majorants of Lévy processes) and apply it to construct a Markov chain in the DCFTP algorithm. We prove that the number of steps taken backwards in time before the coalescence is detected is finite. We analyse numerically the performance of the algorithm (the code, written in Julia 1.0, is available on GitHub).
Item Type: | Journal Article | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Lévy processes , Markov processes , Random walks (Mathematics), Perpetuities , Perfect simulation (Statistics) | ||||||||||||
Journal or Publication Title: | Advances in Applied Probability | ||||||||||||
Publisher: | Applied Probability Trust | ||||||||||||
ISSN: | 0001-8678 | ||||||||||||
Official Date: | December 2019 | ||||||||||||
Dates: |
|
||||||||||||
Volume: | 51 | ||||||||||||
Number: | 4 | ||||||||||||
Page Range: | pp. 967-993 | ||||||||||||
DOI: | 10.1017/apr.2019.39 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | This article has been published in a revised form in Applied Probability Trust ttp://doi.org/XXX]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder. | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Copyright Holders: | © Applied Probability Trust 2019 | ||||||||||||
Date of first compliant deposit: | 29 July 2019 | ||||||||||||
Date of first compliant Open Access: | 23 February 2021 | ||||||||||||
RIOXX Funder/Project Grant: |
|
||||||||||||
Related URLs: | |||||||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year