An analogue of the Berry-Esseen theorem for functionals of weakly ergodic Markov processes

An upper bound is obtained for the rate of convergence in central limit theorem for functionals of weakly ergodic Markov processes that has the rate $O\left(\frac{\ln^{3/2}(n)}{n^{1/4}}\right)$. The approach is based on the one proposed in [1, 2].