2019
Том 71
№ 11

# Moskal'tsova N. V.

Articles: 6
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.

Brief Communications (Russian)

### 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.

Brief Communications (Russian)

### 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 for E-finite bounded functions of ergodic Markov chains. Two useful corollaries are presented.

Brief Communications (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.

Brief Communications (Russian)

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

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

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.

Article (Russian)

### On asymptotics of the potential of a countable ergodic Markov chain

Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 265–269

For a class of functions $f$, the convergence in Abel's sense is proved for the potential \$\sum_{n⩾o}P^nf(i) of a uniform ergodic Markov chain in a countable phase space. Several corollaries are obtained which are useful from the point of view of the possible application to CLT (the central limit theorem) for Markov chains. In particular, we establish the condition equivalent to the boundedness of the second moment for the time of the first return into the state.