210 citations · 240 across the 10 of their papers we have counts for
9 papers · 1 filter
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…
Further studies on square-root boundaries for Bessel processes
Larbi Alili, Hiroyuki Matsumoto
We look at decompositions of perpetuities and apply that to the study of the distributions of hitting times of Bessel processes of two types of square root boundaries. These distri…
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…
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…
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…