Opuscula Math. 43, no. 2 (2023), 145-172
https://doi.org/10.7494/OpMath.2023.43.2.145
Opuscula Mathematica
Square-root boundaries for Bessel processes and the hitting times of radial Ornstein-Uhlenbeck processes
Abstract. This article deals with the first hitting times of a Bessel process to a square-root boundary. We obtain the explicit form of the distribution function of the hitting time by means of zeros of the confluent hypergeometric function with respect to the first parameter. In deducing the distribution function, the time that a radial Ornstein-Uhlenbeck process reaches a certain point is very useful and plays an important role. We also give its distribution function in the case that the starting point is closer to the origin than the arrival site.
Keywords: Bessel process, confluent hypergeometric function, first hitting time, radial Ornstein-Uhlenbeck process, square-root boundary.
Mathematics Subject Classification: 60J60, 33C15, 44A10.
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- Yuji Hamana
https://orcid.org/0000-0002-9997-3114- University of Tsukuba, Department of Mathematics, 1-1-1 Tennodai, Tsukuba 305-8571, Japan
- Communicated by Palle E.T. Jorgensen.
- Received: 2022-10-07.
- Accepted: 2022-12-21.
- Published online: 2023-03-27.
