Abstract
Investigation of sub-gaussian random processes are of special interest since obtained results can be applied to Gaussian processes. In this article the properties of trajectories of a sub-Gaussian process drifted by a curve a studied. The following functionals of extremal type from stochastic process are studied: $\sup_{t\in B}(X(t)-f(t))$, $\inf{t\in B}(X(t)-f(t))$ and $\sup_{t\in B}|X(t)-f(t)|$. An alternative estimate of exceeding by sub-Gaussian process a level, given by a continuous linear curve is obtained. The research is based on the results obtained in the work \cite{yamnenko_vasylyk_TSP_2007}. The results can be applied to such problems of queuing theory and financial mathematics as an estimation of buffer overflow probability and bankruptcy
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