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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
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