Random process from the class $V (\varphi, \psi)$ exceeding a curve

Random processes from the class $V (\varphi, \psi)$ which is more general than the class of $\psi$-sub-Gaussian random process. The upper estimate of the probability that a random process from the class $V (\varphi, \psi)$ exceeds some function is obtained. The results are applied to generalized process of fractional Brownian motion.