# Escape Time of Fractional Brownian Motion

Let $B(t)$ be Brownian motion with $B(0)=x>0$ and let $A>x$. It is well known that the expected time for $B(t)$ to escape the interval $[0,A]$ is equal to $x(A-x)$.

Is the expected time known if the process is a fractional Brownian motion with Hurst exponent $H\in (0,1)$ and $H\neq\frac{1}{2}$?

Since martingale methods fail, not much is know about the distribution of hitting times for the fractional Brownian with parameter $H \neq 1/2$. The hitting time of a level is studied by Decreusefond and Nualart in