On asymptotics of the potential of a countable ergodic Markov chain

• Date: 1993
• Main Authors: Moskal'tsova, N. V., Shurenkov, V. M., Москальцова, Н. В., Шуренков, В. М.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5808
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...