This short communication considers the workload process of a queue operating in slotted time, focusing on the (multivariate) distribution of the workloads at different points in time. In a many-sources framework exact asymptotics are determined, relying on large-deviations results for the sample...

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative errors. Motivated by statistical analysis, we assume...

This short communication considers the workload process of a queue operating in slotted time, focusing on the (multivariate) distribution of the workloads at different points in time. In a many-sources framework exact asymptotics are determined, relying on large-deviations results for the sample...

We consider perpetuities of the form D=B1exp(Y1)+B2exp(Y1+Y2)+⋯, where the Yj’s and Bj’s might be i.i.d. or jointly driven by a suitable Markov chain. We assume that the Yj’s satisfy the so-called Cramér condition with associated root θ∗∈(0,∞) and that the tails of the Bj’s are...

Some important problems of probability and statistics can be reduced to the evaluation of supremum of some homogeneous functional defined on the Strasses ball in the space of smooth functions on the square. We give the solution of this extremal problem in two particular cases: when the...