The Berry-Esseén theorem for strongly mixing Harris recurrent Markov chains

SummaryLet ξ0, ξ1,... be a stationary Harris recurrent Markov chain with state space (E,ℰ), and let f∶ E → IR, Xi=f(ξi). It is known that the sequence Xi, i≧0, is strongly mixing, i.e. α(n)→>0 where α(n) are the strong (or Rosenblatt) mixing coefficients. If α(n) decreases at a sufficiently fast rate and f is suitable, then a central limit holds for the partial sums $$\sum\limits_{i = 0}^n {X_i } $$ . The present paper gives conditions in order that the convergence rates are O(n−1/2).