Geodesic
An alternative method of the proof of the ergodic theorem for general Markov chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 454-467

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As an alternative to the splitting technique of Athreya–Ney and Nummelin, we propose a new method for the proof of ergodic theorems for Markov chains with arbitrary state space. Under our approach, the expansion of the original state space, which, in our opinion, is an ingenious but still artificial technique, can be avoided.
Keywords: splitting method, transition function, Harris condition, state space, ergodic theorem, kernel of an operator.
Mots-clés : Markov chains 
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     author = {S. V. Nagaev},
     title = {An alternative method of the proof of the ergodic theorem for general {Markov} chains},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {454--467},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a2/}
}
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S. V. Nagaev. An alternative method of the proof of the ergodic theorem for general Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 66 (2021) no. 3, pp. 454-467. http://geodesic.mathdoc.fr/item/TVP_2021_66_3_a2/