Bondarev B. V.
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.
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.
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.