I am asked to compare two Brownian Motions which both start at 0, where one is conditioned on the event $B_1 \leq 5$ and one conditioned on $B_1 \geq 5$. After a short amount of time, on, say $[0,dt]$, are you able to tell which is which?
Can I use the independent normal property of Brownian increments to inspect this?
If someone could give me some insight if, they were the same conditions but one brownian motion was $B_t$ and one was a sped of version of that, $B_{\lambda t}$ I'd appreciate it.