On the distribution of storage processes from the class $V(\varphi,\psi)$

Estimates for the distribution of a storage process

$$Q(t)=\sup _{s\le t}\big (X(t)-X(s)-(f(t)-f(s))\big )$$

are obtained in the paper, where $(X(t),t\in T)$ is a stochastic process belonging to the class $V(\varphi ,\psi )$ and where the service output rate $f(t)$ is a continuous function. In particular, the results hold if $(X(t),t\in T)$ is a Gaussian process. Several examples of applications of the results obtained in the paper are given for sub-Gaussian stationary stochastic processes.