Let's say I have a Brownian motion, such that I know its value at time 0 (0) and time T (also 0). I am trying to evaluate the time spent above 0 between time 0 and T.
Obviously I know that the average of this value is 1/2, but is there a way to know the full law of that duration? Or are there other known theoretical results for this? I am guessing this is a fairly common problem but I am unable to find references for this.