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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

Abstract

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.

Keywords

Markov Chain Limit Theorem Centered Frequency Central Limit Central Limit Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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