An explanation of a remarkable identity in law, due to A. Dassios, concerning the $\alpha$-quantile of Brownian motion with drift is given with the help of Bertoin's rearrangement of positive and negative excursions for Brownian motion with drift.
"A Proof of Dassios' Representation of the $|alpha$-Quantile of Brownian Motion with Drift." Ann. Appl. Probab. 5 (3) 757 - 767, August, 1995. https://doi.org/10.1214/aoap/1177004704