Geodesic
On the joint frequency distribution of events in Markov chains with large number of states
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 534-545

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A sequence of simple homogeneous Markov chains is considered. The asymptotic behaviour of the joint distribution law of normalized frequences of events in these chains is investigated when the number of tests $n$ and the number of events $k$ tend to infinity so that $n^{-1}k\ln^3k\to 0$. 
@article{TVP_1977_22_3_a6,
     author = {P. F. Belyaev},
     title = {On the joint frequency distribution of events in {Markov} chains with large number of states},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {534--545},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a6/}
}
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P. F. Belyaev. On the joint frequency distribution of events in Markov chains with large number of states. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 3, pp. 534-545. http://geodesic.mathdoc.fr/item/TVP_1977_22_3_a6/