  In this paper, we consider the long time behaviour of collisionless kinetic
equation with stochastic diffuse boundary operators for velocities bounded away
from zero. We show that under suitable reasonable conditions, the semigroup is
eventually compact. In particular, without any irreducibility assumption, the
semigroup converges exponentially to the spectral projection associated to the
zero eigenvalue as $t \to \infty.$ This contrasts drastically to the case
allowing arbitrarily slow velocities for which the absence of a spectral gap
yields at most algebraic rate of convergence to equilibrium. Some open
questions are also mentioned.
