Random Operators and Stochastic Equations
Editor-in-Chief: Girko, Vyacheslav
Managing Editor: Molchanov, S.
Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre
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Upper estimate of overrunning by Subφ(Ω) random process the level specified by continuous function
In this paper we consider random process from the space Subφ(Ω), which is defined on compact set, and the probability that supremum of this process exceeds some function. The class of Subφ(Ω) random processes is more general than the class of Gaussian processes. By applying obtained estimation to a fluid queue fed by a process of Ornstein-Uhlenbeck from the space strictly Subφ(Ω), where
we show that for interval [a, b] there exist constants A, B, D and
for large enough buffer capacity x.