An arbitrary nonhomogeneous Markov chain with a finite number of states decomposes into asymptotically noncommunicating components that have the mixing property
Teoriâ veroâtnostej i ee primeneniâ, Tome 36 (1991) no. 1, pp. 65-77

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     author = {I. M. Sonin},
     title = {An arbitrary nonhomogeneous {Markov} chain with a finite number of states decomposes into asymptotically noncommunicating components that have the mixing property},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {65--77},
     publisher = {mathdoc},
     volume = {36},
     number = {1},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1991_36_1_a5/}
}
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I. M. Sonin. An arbitrary nonhomogeneous Markov chain with a finite number of states decomposes into asymptotically noncommunicating components that have the mixing property. Teoriâ veroâtnostej i ee primeneniâ, Tome 36 (1991) no. 1, pp. 65-77. http://geodesic.mathdoc.fr/item/TVP_1991_36_1_a5/