## Abstract

Let $\xi_0,\xi_1,\cdots$ be a stationary Harris-recurrent Markov chain with state space $(E,\scr E)$, and let $f\colon E\rightarrow{\bf R}$ and $X_i=f(\xi_i)$. It is known that the sequence $X_i$, $i\geq 0$, is strongly mixing, i.e., $\alpha(n)\rightarrow 0$, where $\alpha(n)$ are the strong (or Rosenblatt) mixing coefficients. If $\alpha(n)$ decreases at a sufficiently fast rate and $f$ is suitably chosen, then a central limit theorem holds for the partial sums $\sum_{i=0}^nX_i$. The present paper gives conditions for the convergence rates to be $O(n^{-1/2})$.