2019
Том 71
№ 6

All Issues

Kovtun E. E.

Articles: 3
Article (Russian)

Order reduction for a system of stochastic differential equations with a small parameter in the coefficient of the leading derivative. Estimate for the rate of convergence

Bondarev B. V., Kovtun E. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 12. - pp. 1587–1601

In the metric $\rho(X, Y) = (\sup\limits_{0 \leq t \leq T} M|X(t) - Y(t)|^2)^{1/2} $ for an ordinary stochastic differential equation of order $p \geq 2$ with small parameter of the higher derivative, we establish an estimate of the rate of convergence of its solution to a solution of stochastic equation of order $p - 1$.

Article (Russian)

A Stochastic Analog of Bogolyubov's Second Theorem

Bondarev B. V., Kovtun E. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 7. - pp. 879–894

We establish an estimate for the rate at which a solution of an ordinary differential equation subject to the action of an ergodic random process converges to a stationary solution of a deterministic averaged system on time intervals of order $e^{1/ερ}$ for some $0 < ρ < 1$.

Article (Russian)

Estimates for the Rate of Convergence in Ordinary Differential Equations under the Action of Random Processes with Fast Time

Bondarev B. V., Kovtun E. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 4. - pp. 435–457

We study the procedure of averaging in the Cauchy problem for an ordinary differential equation perturbed by a certain Markov ergodic process. We establish several estimates for the rate of convergence of solutions of the original problem to solutions of the averaged one.