Fast exact simulation of the first-passage event of a subordinator

Autor:	Cázares, Jorge Ignacio González, Lin, Feng, Mijatović, Aleksandar
Rok vydání:	2023
Předmět:	Mathematics - Probability Statistics - Computation 60G51 65C05
Druh dokumentu:	Working Paper
Popis:	This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-increasing boundary. We prove that the running time of this algorithm has finite moments of all positive orders and give an explicit bound on the expected running time in terms of the L\'evy measure of the subordinator. This bound provides performance guarantees that make our algorithm suitable for Monte Carlo estimation. We provide a GitHub repository with an implementation of the algorithm in Python and Julia. Comment: 22 pages, 6 figures, see https://youtu.be/yQJY-fDBS6Q for a short YouTube presentation describing the results, for GitHub Python and Julia repositories, see https://github.com/fenglin2023/FirstPassageEvent.py and https://github.com/fenglin2023/FirstPassageEvent.jl respectively
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2306.06927 Zobrazit plný text záznamu View this record from Arxiv