I would like to know if there is a formula for the law of $$ \sup_{l \leq t \leq u} \frac{B_t}{\sqrt{t}} $$ where $B$ is a standard Brownian motion, and $0 < l < u < 1$ are constants?
The law of $\sup_{l \leq t \leq u} B_t$ itself is well-known, but I couldn't find in any textbook at hand the law of the quantity that I am interested in..
Thanks for any help in advance!