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An alternative method of the proof of the ergodic theorem for general Markov chains
S. V. Nagaev Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Abstract:
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, Markov chains, ergodic theorem, kernel of an operator.
Received: 21.10.2019 Accepted: 05.03.2021
Citation:
S. V. Nagaev, “An alternative method of the proof of the ergodic theorem for general Markov chains”, Teor. Veroyatnost. i Primenen., 66:3 (2021), 454–467; Theory Probab. Appl., 66:3 (2021), 364–375
Linking options:
https://www.mathnet.ru/eng/tvp5371https://doi.org/10.4213/tvp5371 https://www.mathnet.ru/eng/tvp/v66/i3/p454
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