ИСТИНА

Usually, the models we are trying to explore turn out to be quite complex, and we replace them with simpler ones. But then the problem arises of comparing the quantities of interest in these different models. As a rule, this is done with the help of certain probability inequalities. One of these inequalities is Slepyan's inequality, obtained for the case of multidimensional Gaussian distributions (\cite{Sl}). An analysis of this inequality suggests that it may be true in a more general case. As a result of an Internet search, it turned out that this result has already been proven (\cite{Gupta}). But the existing proof is quite complicated and very precious. We have found a new simpler and more intuitive proof. Further, this generalization is applied to obtain some estimate for the probability of overflow of a large buffer for a telecommunications system with a heterogeneous incoming flow. This research was carried out in accordance with the scientific program of the Moscow Center for Fundamental and Applied Mathematics and Faculty of Computational Mathematics and Cybernetics in Moscow University.