2019
Том 71
№ 10

# Klesov O. I.

Articles: 5
Article (English)

### On the convergence of positive increasing functions to infinity

Ukr. Mat. Zh. - 2010. - 62, № 10. - pp. 1299–1308

We study the conditions of convergence to infinity for some classes of functions extending the well-known class of regularly varying (RV) functions, such as, e.g., $O$-regularly varying (ORV) functions or positive increasing (PI) functions.

Article (English)

### Properties of a Subclass of Avakumović Functions and Their Generalized Inverses

Ukr. Mat. Zh. - 2002. - 54, № 2. - pp. 149-169

We study properties of a subclass of ORV functions introduced by Avakumović and provide their applications for the strong law of large numbers for renewal processes.

Article (Russian)

### Convergence of the series of large-deviation probabilities for sums of independent equally distributed random variables

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 770–784

The series $\sum\nolimits_{n \geqslant 1} {\tau _n P(|S_n | \geqslant \varepsilon n^a )}$ is studied, where $S_n$ are the sums of independent equally distributed random variables, $τ_n$ is a sequence of nonnegative numbers, $α > 0$, and $ɛ > 0$ is an arbitrary positive number. For a broad class of sequences $τ_n$, the necessary and sufficient conditions are established for the convergence of this series for any $ɛ > 0$.

Article (Ukrainian)

### Renewal theorems for random walk with multidimensional time

Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1161–1167

Article (Ukrainian)

### Rate of convergence of series of random variables

Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 309—314