{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/exact-simulation-of-the-extrema-of-stable","title":"Exact Simulation of the Extrema of Stable Processes","arxiv_id":"1806.01870","date":"2018-06-05","proceeding":null,"authors":["Jorge Ignacio González Cázares","Aleksandar Mijatović","Gerónimo Uribe Bravo"],"abstract":"We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpetuity equation for the supremum (via the representation of the concave majorants of L\\'evy 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).","url_abs":"http://arxiv.org/abs/1806.01870v1","url_pdf":"http://arxiv.org/pdf/1806.01870v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"exact-simulation-of-the-extrema-of-stable","repo_url":"https://github.com/jorgeignaciogc/StableSupremum.jl","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"exact-simulation-of-the-extrema-of-stable","repo_url":"https://github.com/jorgeignaciogc/SupStable.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}