Geodesic
The moments of the first entrance into asymptotically retiring domains for ergodic Markov chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 2, pp. 410-420

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We obtain necessary and sufficient conditions for the convergence of moments of the first entrance into asymptotically retiring domains for ergodic Markov chains. 
@article{TVP_1983_28_2_a17,
     author = {D. V. Koroljuk and D. S. Sil'vestrov},
     title = {The moments of the first entrance into asymptotically retiring domains for ergodic {Markov} chains},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {410--420},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_2_a17/}
}
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D. V. Koroljuk; D. S. Sil'vestrov. The moments of the first entrance into asymptotically retiring domains for ergodic Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 2, pp. 410-420. http://geodesic.mathdoc.fr/item/TVP_1983_28_2_a17/