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Remark on the central limit theorem for ergodic chains

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Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain sufficient conditions that should be imposed on a functionf in order that, for ergodic Markov chains, the sum

$$\frac{1}{{\sqrt n }} \sum\limits_{k = 0}^{n - 1} { f(X_k )} $$

be asymptotically normal.

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References

  1. N. V. Moskal'tsova and V. M. Shurenkov, “On potentials of ergodic Markov chains,”Ukr. Mat. Zh.,46, No. 4, 446–449 (1994).

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  2. N. V. Moskal'tsova and V. M. Shurenkov, “Central limit theorem for special classes of functions in ergodic chains,”Ukr. Mat. Zh.,46, No. 8, 1092–1094 (1994).

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  3. V. M. Shurenkov,Ergodic Markov Processes [in Russian], Nauka, Moscow (1989).

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  4. E. Nummelin,General Irreducible Markov Chains and Nonnegative Operators, Cambridge University Press, Cambridge (1984).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    N. V. Moskal'tsova

Authors
  1. N. V. Moskal'tsova
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  2. V. M. Shurenkov
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Additional information

Deceased.

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 118–120, January, 1995.

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Moskal'tsova, N.V., Shurenkov, V.M. Remark on the central limit theorem for ergodic chains. Ukr Math J 47, 138–141 (1995). https://doi.org/10.1007/BF01058805

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  • DOI: https://doi.org/10.1007/BF01058805

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