Heuristic approach to some laws for Brownian motion

Csàki and Vincze have shown that for an elementary tied-down random walk, the pair (maximum, instant of maximum) has the same law as (time spent in (0, 1/2), time spent above 1/2). Formal passage to the limit indicates that the former pair has for a Brownian bridge the same law as (local time at 0, duration of positivity). A quadrivariate density of Karatzas and Shreve and an equivalence for Brownian motion with drift follow.