2017
Том 69
№ 6

All Issues

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

Kozachenko Yu. V., Perestyuk M. M.

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Abstract

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

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 12, pp 1850-1869.

Citation Example: Kozachenko Yu. V., Perestyuk M. M. 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.

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