  The escape from a given domain is one of the fundamental problems in
statistical physics and the theory of stochastic processes. Here, we explore
properties of the escape of an inertial particle driven by L\'evy noise from a
bounded domain, restricted by two absorbing boundaries.Presence of two
absorbing boundaries assures that the escape process can be characterized by
the finite mean first passage time. The detailed analysis of escape kinetics
shows that properties of the mean first passage time for the integrated
Ornstein--Uhlenbeck process driven by L\'evy noise are closely related to
properties of the integrated L\'evy motions which, in turn, are close to
properties of the integrated Wiener process. The extensive studies of the mean
first passage time were complemented by examination of the escape velocity and
energy along with their sensitivity to initial conditions.
