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 $$\frac{1}{{\sqrt n }} \sum\limits_{k = 0}^{n - 1} { f(X_k )} $$ be asymptotically normal.