Olga Vasylyk, Yuriy Kozachenko, Rostyslav Yamnenko
June 1, 2005
In this paper we consider random process from the space Sub φ (Ω) , which is defined on compact set, and the probability that supremum of this process exceeds some function. The class of Sub φ (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 Sub φ (Ω) , where we show that for interval [ a, b ] there exist constants A, B, D and for large enough buffer capacity x .