If we consider a nice Ornstein Uhlenbeck process $d x (t) = - \gamma x(t) dt + \sigma d w (t)$ with $x(0) = x_0 \in (-L,L)$. Here $\gamma, \sigma$ are positive constant and $w(t)$ is a Wiener process.

Is the law of $\tau = \inf \{ t>0, |x(t)| = L \}$ the first hitting time of $\pm L$ by $x(t)$ known explicitly when $x_0 \neq 0$? When $x_0 = 0$, it is not a big issue.

Sorry if the solution is straightforward but it isn't clear to me.

Thanks for help. m.