Opuscula Math. 41, no. 4 (2021), 509-537
https://doi.org/10.7494/OpMath.2021.41.4.509
Opuscula Mathematica
Asymptotic expansions for the first hitting times of Bessel processes
Yuji Hamana
Ryo Kaikura
Kosuke Shinozaki
Abstract. 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.
Keywords: Bessel process, hitting time, tail probability, modified Bessel function, asymptotic expansion, Laplace transform.
Mathematics Subject Classification: 60G40, 60J60, 41A60, 30C10.
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- Yuji Hamana (corresponding author)
https://orcid.org/0000-0002-9997-3114- University of Tsukuba, Institute of Mathematics, 1-1-1 Tennodai, Tsukuba 305-8571, Japan
- Ryo Kaikura
- 1-6-9 Kotohira-honmachi, Kumamoto 860-0814, Japan
- Kosuke Shinozaki
- Leopalace PCOTT205, 2-6-1 Miyauchi, Kawasaki 211-0051, Japan
- Communicated by Palle E.T. Jorgensen.
- Received: 2021-05-10.
- Revised: 2021-06-07.
- Accepted: 2021-06-08.
- Published online: 2021-07-09.
