Chuan Cun YIN
Let X = (Xt)t be a d-dimensional Brownian motion in space Rd(d3), for0 < α, define Bα = {x: x∈Rd,|x| } and Bαb = {x: x ∈Rd,α}.In this paper, we compute the Laplace transforms of the sojourn time of Bα by Xbefore it hitting sphere Bb, the sojourn time of Bαb by X before it hitting Bα andthe sojourn time of Bαb by X before it hitting Bc, respectively. As corollaries, weobtain the Laplace transforms of the hitting time of a sphere by X, the total time Xspends in a bail and the total time X spends in a spherical shell, respectively.
