2019
Том 71
№ 5

All Issues

Samoilenko I. V.

Articles: 9
Article (Ukrainian)

Differential equations with small stochastic summands under the Levy approximating conditions

Nikitin A. V., Samoilenko I. V.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1242-1249

The proposed methods enable us to study a model of stochastic evolution that includes Markov switchings and to identify the diffusion component and big jumps of perturbing process in the limiting equation. Big jumps of this type may describe rare catastrophic events in different applied problems. We consider the case where the perturbation of the system is determined by an impulse process in the nonclassical approximation scheme. Special attention is given to the asymptotic behavior of the generator of the analyzed evolutionary system.

Anniversaries (Ukrainian)

Volodymyr Semenovych Korolyuk (on his 90th birthday)

Bratiichuk N. S., Gusak D. V., Kovalenko I. N., Lukovsky I. O., Makarov V. L., Samoilenko A. M., Samoilenko I. V.

Full text (.pdf)

Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1151-1152

Article (Ukrainian)

Large deviations for impulsive processes in the scheme of Poisson approximation

Samoilenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1526-1535

Asymptotic analysis of the large deviation problem for impulsive processes in the scheme of Poisson approximation is performed. Large deviations for impulsive processes in the scheme of Poisson approximation are defined by an exponential generator for a jump process with independent increments.

Article (Ukrainian)

Convergence of a semi-Markov process and an accompanying

Malik V. F., Samoilenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 5. - pp. 674–681

We propose an approach to the proof of the weak convergence of a semi-Markov process to a Markov process under certain conditions imposed on local characteristics of the semi-Markov process.

Brief Communications (Ukrainian)

Convergence of an impulsive storage process with jump switchings

Samoilenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1282–1286

We investigate an impulsive storage process switched by a jump process. The switching process is, in turn, averaged. We prove the weak convergence of the storage process in the scheme of series where a small parameter ε tends to zero.

Article (Ukrainian)

Asymptotic expansion of a semi-Markov random evolution

Samoilenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1234–1248

We determine the regular and singular components of the asymptotic expansion of a semi-Markov random evolution and show the regularity of boundary conditions. In addition, we propose an algorithm for finding initial conditions for t = 0 in explicit form using the boundary conditions for the singular component of the expansion.

Article (Ukrainian)

Fading Markov Random Evolution

Samoilenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 3. - pp. 364-372

We introduce the notion of fading Markov random evolution and study the properties and characteristics of this process.

Brief Communications (Russian)

Moments of Markov Random Evolutions

Samoilenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 1002-1008

We find moments of a process of Markov random evolutions in a finite-dimensional space.

Brief Communications (Russian)

A Probability Method for the Solution of the Telegraph Equation with Real-Analytic Initial Conditions

Samoilenko I. V., Turbin A. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1127-1134

We propose a method for the construction of an analytic solution of the Cauchy problem for the telegraph equation that is based on its simulation by a one-dimensional Markov random evolution.