2019
Том 71
№ 8

All Issues

Perestyuk M. M.

Articles: 2
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 $P\left\{ \sup\cfrac{X (t)}{c(t)} > \varepsilon\right\}, \quad \varepsilon > 0$..