TY  - JOUR
ID  - Hamana2023
LB  - Hamana2023
AU  - Hamana, Yuji
TI  - Square-root boundaries for Bessel processes and the hitting times of radial Ornstein-Uhlenbeck processes
ST  - Square-root boundaries for Bessel processes and the hitting times of radial Ornstein-Uhlenbeck processes
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 2
SP  - 145
EP  - 172
DO  - https://doi.org/10.7494/OpMath.2023.43.2.145
UR  - https://doi.org/10.7494/OpMath.2023.43.2.145
AB  - 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.
KW  - Bessel process
KW  - confluent hypergeometric function
KW  - first hitting time
KW  - radial Ornstein-Uhlenbeck process
KW  - square-root boundary
SN  - 1232-9274
ER  -