In this paper, we examine the Renyi entropy rate of stationary ergodic
processes. For a special class of stationary ergodic processes, we prove that
the Renyi entropy rate always exists and can be polynomially approximated by
its defining sequence; moreover, using the Markov approximation method, we show
that the Renyi entropy rate can be exponentially approximated by that of the
Markov approximating sequence, as the Markov order goes to infinity. For the
general case, by constructing a counterexample, we disprove the conjecture that
the Renyi entropy rate of a general stationary ergodic process always converges
to its Shannon entropy rate as {\alpha} goes to 1