2018
Том 70
№ 5

All Issues

Kozachenko Yu. V.

Articles: 9
Article (Ukrainian)

On the uniform convergence of wavelet expansions of random processes from Orlicz spaces of random variables. II

Kozachenko Yu. V., Perestyuk M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 6. - pp. 759–775

We establish conditions under which wavelet expansions of random processes from Orlicz spaces of random variables converge uniformly with probability one on a bounded interval.

Article (Ukrainian)

On the uniform convergence of wavelet expansions of random processes from Orlicz spaces of random variables. I

Kozachenko Yu. V., Perestyuk M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1647–1660

We establish conditions under which there exists a function c(t) > 0 such that $\sup\cfrac{X (t)}{c(t)} < \infty$, where X(t) is a random process from an Orlicz space of random variables. We obtain estimates for the probabilities $P\left\{ \sup\cfrac{X (t)}{c(t)} > \varepsilon\right\}, \quad \varepsilon > 0$..

Article (Ukrainian)

Random processes in Sobolev-Orlicz spaces

Kozachenko Yu. V., Yakovenko T. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1340–1356

We establish conditions under which the trajectories of random processes from Orlicz spaces of random variables belong with probability one to Sobolev-Orlicz functional spaces, in particular to the classical Sobolev spaces defined on the entire real axis. This enables us to estimate the rate of convergence of wavelet expansions of random processes from the spaces $L_P({\Omega})$ and $L_2({\Omega})$ in the norm of the space $L_q(\mathbb{R})$.

Anniversaries (Ukrainian)

Mykhailo Iosypovych Yadrenko (On His 70th Birthday)

Buldygin V. V., Korolyuk V. S., Kozachenko Yu. V., Mitropolskiy Yu. A., Perestyuk N. A., Portenko N. I., Samoilenko A. M., Skorokhod A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 4. - pp. 435-438

Article (Ukrainian)

Estimation of Parameters of Homogeneous Gaussian Random Fields

Kozachenko Yu. V., Kurchenko О. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 8. - pp. 1082-1088

On the basis of the limit theorem for quadratic variation, we construct a consistent estimator for parameters of a homogeneous Gaussian random field of a certain class. We find confidence ellipsoids for estimators of this sort.

Article (Ukrainian)

Estimates of the supremum distribution for a certain class of random processes

Buldygin V. V., Kozachenko Yu. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1993. - 45, № 5. - pp. 596–608

Exponential estimates of the “tails” of supremum distributions are obtained for a certain class of pre-Gaussian random processes. The results obtained are applied to the quadratic forms of Gaussian processes and to processes representable as stochastic integrals of processes with independent increments.

Article (Ukrainian)

Some properties of random processes in Banach Kσ-spaces

Abzhanov E. A., Kozachenko Yu. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 275–280

Article (Ukrainian)

Sub-Gaussian random variables

Buldygin V. V., Kozachenko Yu. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 6. - pp. 723–730

Article (Ukrainian)

Local properties of the trajectories of certain random functions

Kozachenko Yu. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1967. - 19, № 2. - pp. 109–116