Abstract
For a class of functionsf, the convergence in Abel's sense is proved for the potential ⌆n⩾o P n f(i) of a uniform ergodic Markov chain in a countable phase space. Several corollaries are obtained which are useful from the point of view of the possible application to CLT (the central limit theorem) for Markov chains. In particular, we establish the condition equivalent to the boundedness of the second moment for the time of the first return into the state.
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Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 2, pp. 265–269, February, 1993.
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Moskal'tsova, N.V., Shurenkov, V.M. On asymptotics of the potential of a countable ergodic Markov chain. Ukr Math J 45, 284–289 (1993). https://doi.org/10.1007/BF01060985
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DOI: https://doi.org/10.1007/BF01060985