Exact Solution to the Mean Exit Time Problem for Free Inertial Processes Driven by Gaussian White Noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, $T(x,v)$, of a free inertial process driven by Gaussian white noise from a region $(0,L)$ in space. We obtain a completely explicit expression for $T(x,0\mathrm{})$ and discuss the dependence of $T(x,v)$ as a function of the size $L$ of the region. We develop a new method that may be used to solve other exit time problems.