Том 71
№ 9

All Issues

Nikitin A. V.

Articles: 2
Article (Ukrainian)

Differential equations with small stochastic summands under the Levy approximating conditions

Nikitin A. V., Samoilenko I. V.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Asymptotics of normalized control with Markov switchings

Khimka U. T., Nikitin A. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 8. - pp. 1092-1101

We study the process of transfer of Markov perturbations and control over this process under the condition of existence of the equilibrium point of the quality criterion. For this control, we construct a normalized process and establish its asymptotic normality in the form of the Ornstein – Uhlenbeck process in the case where the transfer process changes under the influence of Markov switchings along a new trajectory of evolution from the state in which it was at the time of switching.