Endzhyrgly, M. V. Estimation of the probability of exceeding a given level by a random series. (English. Russian original) Zbl 0835.60029 Theory Probab. Math. Stat. 47, 23-28 (1993); translation from Teor. Jmovirn. Mat. Stat. 47, 23-29 (1992). Summary: Certain estimates are obtained for the probability of exceeding a given level by a random process \(\xi (t) = \sum^\infty_{k = 1} f_k(t) \xi_k\), where the random variables \(\xi_k\) jointly belong to the space \(\overline {\text{Sub}}_\varphi (\Omega)\), a Banach space of sub-Gaussian random variables, under conditions ensuring the uniform convergence of the series. MSC: 60G15 Gaussian processes 60E15 Inequalities; stochastic orderings 40A30 Convergence and divergence of series and sequences of functions Keywords:probability of exceeding a given level; uniform convergence PDFBibTeX XMLCite \textit{M. V. Endzhyrgly}, Theory Probab. Math. Stat. 47, 1 (1992; Zbl 0835.60029); translation from Teor. Jmovirn. Mat. Stat. 47, 23--29 (1992)