On asymptotics of the potential of a countable ergodic Markov chain
For a class of functions $f$, the convergence in Abel's sense is proved for the potential $\sum_{n⩾o}P^nf(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...
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| Datum: | 1993 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1993
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5808 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | For a class of functions $f$, the convergence in Abel's sense is proved for the potential $\sum_{n⩾o}P^nf(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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