Yuji Hamana, Hiroyuki Matsumoto
Published 2023-01-10Version 1
Let $S^{d-1}_r$ be the sphere in $\bR^d$ whose center is the origin and the radius is $r$, and $\sigma_r$ be the first hitting time to it of the standard Brownian motion $\{B_t\}_{t\geqq0}$, possibly with constant drift. The aim of this article is to show explicit formulae by means of spherical harmonics for the density of the joint distribution of $(\sigma_r,B_{\sigma_r})$ and to study the asymptotic behavior of the distribution function.
Perpetual integral functionals of diffusions and their numerical computations
Hitting times to spheres of Brownian motions with and without drifts
An elementary proof that the first hitting time of an $F_σ$ set by a jump process is a stopping time
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