Geodesic
An analogue of the Berry-Esseen theorem for functionals of weakly ergodic Markov processes
Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 53-63.

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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].
Keywords: Markov process, corrector, weak ergodicity. 
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G. M. Molyboga. An analogue of the Berry-Esseen theorem for functionals of weakly ergodic Markov processes. Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 53-63. http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a5/

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