2019
Том 71
№ 7

All Issues

Klesov O. I.

Articles: 5
Article (English)

On the convergence of positive increasing functions to infinity

Buldygin V. V., Klesov O. I., Steinebach J. G.

↓ Abstract   |   Full text (.pdf)

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

Buldygin V. V., Klesov O. I., Steinebach J. G.

↓ Abstract   |   Full text (.pdf)

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 (Ukrainian)

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

Klesov O. I.

↓ Abstract   |   Full text (.pdf)

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 Sn are the sums of independent equally distributed random variables, ?n is a sequence of nonnegative numbers, ?>0, and ?>0 is an arbitrary positive number. For a broad class of sequences ?n, the necessary and sufficient conditions are established for the convergence of this series for any ?>0.

Article (Ukrainian)

Renewal theorems for random walk with multidimensional time

Klesov O. I.

Full text (.pdf)

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

Article (Ukrainian)

Rate of convergence of series of random variables

Klesov O. I.

Full text (.pdf)

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