16 citations · 30 across the 8 of their papers we have counts for
8 papers
Brownian Hitting to Spheres
Yuji Hamana, Hiroyuki Matsumoto
Let be the sphere in $\bR^d$ whose center is the origin and the radius is , and be the first hitting time to it of the standard Brownian motion $\{B_t\}_{t\geq…
A formula for the expected volume of the Wiener sausage with constant drift
Yuji Hamana, Hiroyuki Matsumoto
We consider the Wiener sausage for a Brownian motion with a constant drift up to time associated with a closed ball. In the two or more dimensional cases, we obtain the explici…
Hitting times to spheres of Brownian motions with and without drifts
Yuji Hamana, Hiroyuki Matsumoto
Explicit formulae for the densities of the first hitting times to the sphere of Brownian motions with drifts are given. We need to consider the joint distributions of the first hit…
Asymptotic expansion of the expected volume of the Wiener sausage in even dimensions
Yuji Hamana
We consider the Wiener sausage for a Brownian motion up to time associated with a closed ball in even dimensional cases. We obtain the asymptotic expansion of the expected volu…
Asymptotics of the probability distributions of the first hitting times of Bessel processes
Yuji Hamana, Hiroyuki Matsumoto
The asymptotic behavior of the tail probabilities for the first hitting times of the Bessel process with arbitrary index is shown without using the explicit expressions for the dis…
On the zeros of the Macdonald functions
Yuji Hamana, Hiroyuki Matsumoto, Tomoyuki Shirai
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…
Hitting times of Bessel processes, volume of Wiener sausages and zeros of Macdonald functions
Yuji Hamana, Hiroyuki Matsumoto
We derive formulae for some ratios of the Macdonald functions, which are simpler and easier to treat than known formulae. The result gives two applications in probability theory. O…
The probability densities of the first hitting times of Bessel processes
Yuji Hamana, Hiroyuki Matsumoto
We are concerned with the first hitting times of the Bessel processes. We give explicit expressions for the densities by means of the zeros of the Bessel functions and show their a…