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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board: 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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Volume 13, Issue 2


Upper estimate of overrunning by Subφ(Ω) random process the level specified by continuous function

Olga Vasylyk / Yuriy Kozachenko / Rostyslav Yamnenko

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.

Key Words: φ-sub-Gaussian stochastic process;; metric entropy;; supremum distribution;; process of Ornstein-Uhlenbeck.

About the article

Published in Print: 2005-06-01

Citation Information: Random Operators and Stochastic Equations rose, Volume 13, Issue 2, Pages 111–128, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/156939705323383832.

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