2019
Том 71
№ 11

All Issues

Bondarev B. V.

Articles: 3
Article (Russian)

Bernstein inequality under averaging of elliptic systems in periodic random media

Bondarev B. V., Korolev M. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 12. - pp. 1638-1650

We construct the exponential Bernstein inequality for normed fluctuations of a solution of the Dirichlet problem with rapidly oscillating periodic random coefficients with respect to a solution of the averaged Dirichlet problem.

Article (Russian)

Some properties of multiparameter random fields

Bondarev B. V., Zhirnyi G. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1995. - 47, № 12. - pp. 1609–1621

We study some properties of multiparameter random fields, namely, the problems of absolute continuity of measures and averaging in the multiparameter case. For a special stochastic system, we present inequalities of large deviations.

Article (Russian)

Diffusion approximation of normalized integrals of weakly dependent processes and its applications

Bondarev B. V., Shurko I. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 11. - pp. 1449–1466

We obtain exact estimates for the rate of convergence of normalized integrals of weakly dependent stationary processes to the standard Wiener process in the uniform metric in probability. These estimates are then applied to the investigation of the behavior of stochastic systems with curvilinear boundaries subjected to the action of weakly dependent random perturbations.