  We consider a stochastic billiard in a random tube which stretches to
infinity in the direction of the first coordinate. This random tube is
stationary and ergodic, and also it is supposed to be in some sense well
behaved. The stochastic billiard can be described as follows: when strictly
inside the tube, the particle moves straight with constant speed. Upon hitting
the boundary, it is reflected randomly, according to the cosine law: the
density of the outgoing direction is proportional to the cosine of the angle
between this direction and the normal vector. We also consider the
discrete-time random walk formed by the particle's positions at the moments of
hitting the boundary. Under the condition of existence of the second moment of
the projected jump length with respect to the stationary measure for the
environment seen from the particle, we prove the quenched invariance principles
for the projected trajectories of the random walk and the stochastic billiard.
