Geodesic
Mixing Conditions for Markov Chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 321-338

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In the paper, simple sufficient conditions are obtained for a homogeneous recurrent Markov chain with an arbitrary state space to possess the strong mixing property. These conditions enable constructing various examples of stationary processes with strong mixing property for which the central limit theorem fails to hold. For the examples constructed, the growth of the variance of partial sums and the decrease of the mixing coefficient are estimated. 
@article{TVP_1973_18_2_a8,
     author = {Yu. A. Davydov},
     title = {Mixing {Conditions} for {Markov} {Chains}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {321--338},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a8/}
}
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Yu. A. Davydov. Mixing Conditions for Markov Chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 2, pp. 321-338. http://geodesic.mathdoc.fr/item/TVP_1973_18_2_a8/