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Donsker theorems for diffusions: Necessary and sufficient conditions
Aad van der Vaart, Harry van Zanten
We consider the empirical process G_t of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions,…
A large-deviations analysis of the GI/GI/1 SRPT queue
Misja Nuyens, Bert Zwart
We consider a GI/GI/1 queue with the shortest remaining processing time discipline (SRPT) and light-tailed service times. Our interest is focused on the tail behavior of the sojour…
Sample-path large deviations for tandem and priority queues with Gaussian inputs
Michel Mandjes, Miranda van Uitert
This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (tw…
Krein's spectral theory and the Paley-Wiener expansion for fractional Brownian motion
Kacha Dzhaparidze, Harry van Zanten
In this paper we develop the spectral theory of the fractional Brownian motion (fBm) using the ideas of Krein's work on continuous analogous of orthogonal polynomials on the unit c…