For $d$-dimensional Brownian motion starting at 0 and having constant drift it is shown that the interarrival times between successive concentric spheres and the hitting place on the outermost sphere are independent. This generalizes results of Kent and Stern. A discrete analogue extending Samuels' theorem is indicated.
"An Independence Property of Brownian Motion with Drift." Ann. Probab. 8 (3) 600 - 601, June, 1980. https://doi.org/10.1214/aop/1176994729