2019
Том 71
№ 11

# Kozachenko Yu. V.

Articles: 13
Article (Ukrainian)

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

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

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

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)

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

Article (Ukrainian)

### Estimation of Parameters of Homogeneous Gaussian Random Fields

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 (Russian)

### Impulsive boundary-value problems for weakly nonlinear systems with control

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 910–917

For weakly nonlinear impulsive differential systems with control, we obtain necessary and sufficient conditions for the existence of control and the corresponding solutions of differential systems with general boundary conditions.

Article (Ukrainian)

### Distribution of the supremum of random processes from quasi-Banach $K_{σ}$-spaces

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 918-930

We study random processes from quasi-Banach $K_{σ}$-spaces of random variables whose domain of definition is not necessarily a compact set. We establish conditions under which the supremum of a properly normalized process belongs to the same space as the process itself. We also obtain estimates for the norm of this supremum.

Article (Russian)

### Boundary-value problems with random initial conditions and functional series from subφ (Ω). II

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 897–906

We study conditions for convergence and the rate of convergence of random functional series from the space subφ(Ω) in various norms. The results obtained are applied to the investigation of a boundary-value problem for a hyperbolic equation with random initial conditions.

Article (Russian)

### Boundary-Value problems with random initial conditions and functional series from subφ (Ω). I

Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 504–515

We study conditions for convergence and the rate of convergence of random functional series from the space subφ (Ω) in various norms. The results are applied to the investigation of a boundary-value problem for a hyperbolic equation with random initial conditions.

Article (Russian)

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

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

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

Article (Ukrainian)

### Sub-Gaussian random variables

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

Article (Ukrainian)

### Local properties of the trajectories of certain random functions

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