Ukrainian Mathematical Journal

, Volume 45, Issue 12, pp 1928–1931 | Cite as

Central limit theorem for centered frequencies of a countable ergodic markov chain

  • N. V. Moskal'tsova
  • V. M. Shurenkov
Brief Communications


On the basis of results concerning the behavior of the potential of a countable ergodic Markov chain for a certain class of functions, the asymptotic normality of the variable\(\tfrac{1}{{\sqrt n }}\sum\nolimits_{k = 0}^{n - 1} {f(X_k )} \) is proved. The asymptotic normality of centered frequencies is obtained without using the condition of finiteness of the timeM0τ2 of the first return to a chain state.


Markov Chain Limit Theorem Centered Frequency Central Limit Central Limit Theorem 
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  1. 1.
    N. V. Moskal'tsova and V. M. Shurenkov, “On the asymptotics of the potential of a countable ergodic Markov chain,”Ukr. Mat. Zh.,45, No. 2, 265–270 (1993).Google Scholar
  2. 2.
    V. M. Shurenkov,Ergodic Markov Processes [in Russian], Nauka, Moscow (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • N. V. Moskal'tsova
    • 1
  • V. M. Shurenkov
  1. 1.Donetsk UniversityDonetsk

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