Browsing by Author "Hamana, Yuji"

Now showing 1 - 4 of 4

Access status: Open Access ,
Asymptotic expansions for the first hitting times of Bessel processes
(Wydawnictwa AGH, 2021) Hamana, Yuji; Kaikura, Ryo; Shinozaki, Kosuke
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.
Access status: Open Access ,
On the zeros of the Macdonald functions
(Wydawnictwa AGH, 2019) Hamana, Yuji; Matsumoto, Hiroyuki; Shirai, Tomoyuki
We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior of the zeros when the index moves. Results by numerical computations are also presented.
Access status: Open Access ,
Square-root boundaries for Bessel processes and the hitting times of radial Ornstein-Uhlenbeck processes
(Wydawnictwa AGH, 2023) Hamana, Yuji
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.
Access status: Open Access ,
Tail probability of the hitting time of Brownian motion to a sphere with fixed hitting sites
(Wydawnictwa AGH, 2025) Hamana, Yuji
We consider $d$-dimensional Brownian motion $\{B_\mu(t)\}_{t\geqq0}$ with a drift $\mu\in\mathbb{R}^d$ and the first hitting time $\sigma_{r,\mu}^{(d)}$ to the sphere with radius $r$ centered at the origin. This article deals with asymptotic behavior of the probability that both $t\lt\sigma_{r,\mu}^{(d)}\lt\infty$ and $B_\mu(\sigma_{r,\mu}^{(d)})\in A$ occur simultaneously, and we obtain that this probability admits an asymptotic expansion in powers of $1/t$ if $d\geqq3$ and in that of $1/\log t$ if $d=2$ for large $t$. Moreover, we investigate the case of Brownian motion with no drift.