Asymptotic expansions for the first hitting times of Bessel processes

We study a precise asymptotic behavior of the tail probability of the first hitting time of the Bessel process. We deduce the order of the third term and decide the explicit form of its coefficient.

Bibliographic Details
Main Authors:	Yuji Hamana, Ryo Kaikura, Kosuke Shinozaki
Format:	Article
Language:	English
Published:	AGH Univeristy of Science and Technology Press 2021-07-01
Series:	Opuscula Mathematica
Subjects:	bessel process hitting time tail probability modified bessel function asymptotic expansion laplace transform
Online Access:	https://www.opuscula.agh.edu.pl/vol41/4/art/opuscula_math_4125.pdf

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spelling	doaj-c9dde270a89344d89ce7bbcbb97206b32021-07-09T22:48:13ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742021-07-01414509537https://doi.org/10.7494/OpMath.2021.41.4.5094125Asymptotic expansions for the first hitting times of Bessel processesYuji Hamana0https://orcid.org/0000-0002-9997-3114Ryo Kaikura1Kosuke Shinozaki2University of Tsukuba, Institute of Mathematics, 1-1-1 Tennodai, Tsukuba 305-8571, Japan1-6-9 Kotohira-honmachi, Kumamoto 860-0814, JapanLeopalace PCOTT205, 2-6-1 Miyauchi, Kawasaki 211-0051, JapanWe study a precise asymptotic behavior of the tail probability of the first hitting time of the Bessel process. We deduce the order of the third term and decide the explicit form of its coefficient.https://www.opuscula.agh.edu.pl/vol41/4/art/opuscula_math_4125.pdfbessel processhitting timetail probabilitymodified bessel functionasymptotic expansionlaplace transform
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yuji Hamana Ryo Kaikura Kosuke Shinozaki
spellingShingle	Yuji Hamana Ryo Kaikura Kosuke Shinozaki Asymptotic expansions for the first hitting times of Bessel processes Opuscula Mathematica bessel process hitting time tail probability modified bessel function asymptotic expansion laplace transform
author_facet	Yuji Hamana Ryo Kaikura Kosuke Shinozaki
author_sort	Yuji Hamana
title	Asymptotic expansions for the first hitting times of Bessel processes
title_short	Asymptotic expansions for the first hitting times of Bessel processes
title_full	Asymptotic expansions for the first hitting times of Bessel processes
title_fullStr	Asymptotic expansions for the first hitting times of Bessel processes
title_full_unstemmed	Asymptotic expansions for the first hitting times of Bessel processes
title_sort	asymptotic expansions for the first hitting times of bessel processes
publisher	AGH Univeristy of Science and Technology Press
series	Opuscula Mathematica
issn	1232-9274
publishDate	2021-07-01
description	We study a precise asymptotic behavior of the tail probability of the first hitting time of the Bessel process. We deduce the order of the third term and decide the explicit form of its coefficient.
topic	bessel process hitting time tail probability modified bessel function asymptotic expansion laplace transform
url	https://www.opuscula.agh.edu.pl/vol41/4/art/opuscula_math_4125.pdf
work_keys_str_mv	AT yujihamana asymptoticexpansionsforthefirsthittingtimesofbesselprocesses AT ryokaikura asymptoticexpansionsforthefirsthittingtimesofbesselprocesses AT kosukeshinozaki asymptoticexpansionsforthefirsthittingtimesofbesselprocesses
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Asymptotic expansions for the first hitting times of Bessel processes

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