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December 2018 Precise Asymptotic Formulae for the First Hitting Times of Bessel Processes
Yuji HAMANA, Hiroyuki MATSUMOTO
Tokyo J. Math. 41(2): 603-615 (December 2018). DOI: 10.3836/tjm/1502179246

Abstract

We study the first hitting time to $b$ of a Bessel process with index $\nu$ starting from $a$, which is denoted by $\tau_{a,b}^{(\nu)}$, in the case when $0<b<a$. When $\nu>1$ and $\nu-1/2$ is not an integer, we obtain that $\mathbf P(t<\tau_{a,b}^{(\nu)}<\infty)$ is asymptotically equal to $\kappa_1^{(\nu)}t^{-\nu}+\kappa_2^{(\nu)} t^{-\nu-1}$ as $t\to\infty$ for some explicit constants $\kappa_1^{(\nu)}$ and $\kappa_2^{(\nu)}$. The constant $\kappa_1^{(\nu)}$ is known and the aim is to get $\kappa_2^{(\nu)}$. Combining our result with the known facts, we obtain the precise asymptotic formula for every index $\nu$.

Citation

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Yuji HAMANA. Hiroyuki MATSUMOTO. "Precise Asymptotic Formulae for the First Hitting Times of Bessel Processes." Tokyo J. Math. 41 (2) 603 - 615, December 2018. https://doi.org/10.3836/tjm/1502179246

Information

Published: December 2018
First available in Project Euclid: 20 November 2017

zbMATH: 07053495
MathSciNet: MR3908813
Digital Object Identifier: 10.3836/tjm/1502179246

Subjects:
Primary: 60G40
Secondary: 60J60

Rights: Copyright © 2018 Publication Committee for the Tokyo Journal of Mathematics

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Vol.41 • No. 2 • December 2018
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