2017
Том 69
№ 9

# Kozachenko Yu. V.

Articles: 8
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)

### 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