  We prove the existence of limiting distributions for a large class of Markov
chains on a general state space in a random environment. We assume suitable
versions of the standard drift and minorization conditions. In particular, the
system dynamics should be contractive on the average with respect to the
Lyapunov function and large enough small sets should exist with large enough
minorization constants. We also establish that a law of large numbers holds for
bounded functionals of the process. Applications to queuing systems, to machine
learning algorithms and to autoregressive processes are presented.
