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

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