2019
Том 71
№ 11

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

Moskal'tsova N. V., Shurenkov V. M.

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Abstract

On the basis of results relating to the behavior of the potential of a countable ergodic Markov chain, for a certain class of functions, the asymptotic normality of a variable $\cfrac{1}{\sqrt{n}}\sum^{n-1}_{k=0}f(X_k)$ for $n \rightarrow \infty$ has been proved. The asymptotic normality of the centering frequencies has been obtained without using the finileness conditions for the time $M_0\tau^2$ of the first return into a chain state.

English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 12, pp 1928-1931.

Citation Example: Moskal'tsova N. V., Shurenkov V. M. Central limit theorem for centered frequencies of a countable ergodic markov chain // Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1713–1715.

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