  We study a general class of random walks driven by a uniquely ergodic
Markovian environment. Under a coupling condition on the environment we obtain
strong ergodicity properties for the environment as seen from the position of
the walker, that is, the environment process. We can transfer the rate of
mixing in time of the environment to the rate of mixing of the environment
process with a loss of at most polynomial order. Therefore the method is
applicable to environments with sufficiently fast polynomial mixing. We obtain
unique ergodicity of the environment process. Moreover, the unique invariant
measure of the environment process depends continuously on the jump rates of
the walker. As a consequence we obtain the law of large numbers and a central
limit theorem with nondegenerate variance for the position of the walk.
