  We obtain non-Gaussian limit laws for one-dimensional random walk in a random
environment assuming that the environment is a function of a stationary Markov
process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for
random walks in i.i.d. environments. The basic assumption is that the
underlying Markov chain is irreducible and either with a finite state space or
with the transition kernel dominated above and below by a probability measure.
