2019
Том 71
№ 8

All Issues

Korolev M. E.

Articles: 2
Article (Russian)

Functional law of iterated logarithm for normalized integrals of processes with weak dependence

Bondarev B. V., Korolev M. E.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 490–499

For normalized integrals of processes with weak dependence, we prove the law of iterated logarithm in the Strassen form. The results obtained are used for the construction of a curvilinear confidence region in which a solution of an equation with small parameter is sought.

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.