What is the mean of the stopping time for a Brownian Motion to reach either 1 or -1?
My thoughts: It can be seen that $B_{t}^2 - t$ is a Martingale. And we can somehow use $E[B_{T}^2 - T\mid F_{0}] = 0$ where $T=\min\{t:B_{t}=1\mbox{ or } -1\}$, but I don't know where to go from here.
Thanks