2019
Том 71
№ 8

# Moskal'tsova N. V.

Articles: 5
Brief Communications (Russian)

### Remark on the central limit theorem for ergodic chains

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 118-120

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.

Article (Ukrainian)

### Central limit theorem for stochastically additive functionals of ergodic chains

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1421–1423

A central limit theorem is proved for stochastically additive functional of ergodic Markov chains.

Article (Ukrainian)

### Central limit theorem for special classes of functions of ergodic chains

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1092–1094

A central limit theorem is proved forE-finite bounded functions of ergodic Markov chains. Two useful corollaries are presented.

Article (Ukrainian)

### On potentials of ergodic Markov chains

Ukr. Mat. Zh. - 1994. - 46, № 4. - pp. 446–449

Two theorems on the existence of the potential of an ergodic Markov chain in an arbitrary phase space are proved.

Article (Ukrainian)

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

Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1713–1715