The Berry-Esseen theorem for functionals of discrete Markov chains

Summary The error bound O(1/n) is derived in the central limit theorem for partial sums where _j is a recurrent discrete Markov chain and f is a real valued function on the state space. In particular it is shown that for bounded f and starting distribution dominated by some multiple of the stationary one, it is sufficient for the chain to have recurrence times with third moments on order to get this bound.