ASYMPTOTIC EXPANSIONS FOR THE FIRST HITTING TIMES OF BESSEL PROCESSES

被引：2
|
作者：
Hamana, Yuji [1 ]
Kaikura, Ryo [2 ]
Shinozaki, Kosuke [3 ]
机构：
[1] Univ Tsukuba, Inst Math, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058571, Japan
[2] 1-6-9 Kotohira Honmachi, Kumamoto 8600814, Japan
[3] Leopalace PCOTT205,2-6-1 Miyauchi, Kawasaki, Kanagawa 2110051, Japan
来源：
OPUSCULA MATHEMATICA | 2021年 / 41卷 / 04期
基金：
日本学术振兴会;
关键词：
Bessel process; hitting time; tail probability; modified Bessel function; asymptotic expansion; Laplace transform; PROBABILITY-DISTRIBUTIONS; FORMULAS;
D O I：
10.7494/OpMath.2021.41.4.509
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：509 / 537
页数：29
相关论文
共 50 条
  • [31] Optimal Design for Estimation in Diffusion Processes from First Hitting Times
    Iolov, Alexandre
    Ditlevsen, Susanne
    Longtin, Andr
    SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2017, 5 (01): : 88 - 110
  • [32] Moments of first hitting times for birth-death processes on trees
    Yuhui Zhang
    Frontiers of Mathematics in China, 2019, 14 : 833 - 854
  • [33] First hitting times for doubly skewed Ornstein-Uhlenbeck processes
    Song, Shiyu
    Wang, Suxin
    Wang, Yongjin
    STATISTICS & PROBABILITY LETTERS, 2015, 96 : 212 - 222
  • [34] Asymptotic expansions for the radii of starlikeness of normalised Bessel functions
    Baricz, Arpad
    Nemes, Gergo
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 494 (02)
  • [35] 1ST HITTING TIME FOR BESSEL PROCESSES
    TAKEUCHI, J
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1985, 61 (08) : 246 - 248
  • [36] Unimodality of Hitting Times for Stable Processes
    Letemplier, Julien
    Simon, Thomas
    SEMINAIRE DE PROBABILITES XLVI, 2014, 2123 : 345 - 357
  • [37] Mixing times and hitting times for general Markov processes
    Anderson, Robert M.
    Duanmu, Haosui
    Smith, Aaron
    ISRAEL JOURNAL OF MATHEMATICS, 2023,
  • [38] HITTING TIMES FOR TRANSIENT STABLE PROCESSES
    PORT, SC
    PACIFIC JOURNAL OF MATHEMATICS, 1967, 21 (01) : 161 - &
  • [39] The probability distributions of the first hitting times of radial Ornstein-Uhlenbeck processes
    Hamana, Yuji
    STUDIA MATHEMATICA, 2020, 251 (01) : 65 - 88
  • [40] Review and implementation of cure models based on first hitting times for Wiener processes
    Jeremy Balka
    Anthony F. Desmond
    Paul D. McNicholas
    Lifetime Data Analysis, 2009, 15
12345