Remark on the central limit theorem for ergodic chains - Moskal'tsova, N. V.; Shurenkov, V. M. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
We obtain sufficient conditions that should be imposed on a functionf in order that, for ergodic Markov chains, the sum 1n _k = 0^n - 1 f(X_k ) be asymptotically normal.