Showing papers by "Krzysztof Dębicki published in 2011"
TL;DR: In this article, the exact asymptotics of the supremum distribution of fractional Laplace motion were derived for a centered Gaussian process with stationary increments and variance function.
Abstract: Let $\{X(t) :t∈[0, ∞)\}$ be a centered Gaussian process with stationary increments and variance function $σ_X^2(t)$. We study the exact asymptotics of $ℙ(\sup _{t∈[0, T]}X(t)>u)$ as $u→∞$, where $T$ is an independent of $\{X(t)\}$ non-negative Weibullian random variable. As an illustration, we work out the asymptotics of the supremum distribution of fractional Laplace motion.
50 citations
14 citations
TL;DR: This work addresses the problem of characterizing the correlation structure of the stationary buffer content process, the speed of convergence to stationarity, and analysis of an asymptotic constant associated with the stationarybuffer content distribution (the so-called Pickands constant).
Abstract: We present three challenging open problems that originate from the analysis of the asymptotic behavior of Gaussian fluid queueing models. In particular, we address the problem of characterizing the correlation structure of the stationary buffer content process, the speed of convergence to stationarity, and analysis of an asymptotic constant associated with the stationary buffer content distribution (the so-called Pickands constant).
11 citations
TL;DR: In this paper, the authors investigated Gaussian queues in the light-traffic and in the heavy traffic regime, and showed that under mild regularity conditions on the variance function, there exists a normalizing function such that the stationary workload process converges to a non-trivial limit.
Abstract: In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process $X\equiv\{X(t):t\in\mathbb R\}$ with stationary increments and variance function $\sigma^2_X(\cdot)$, equipped with a deterministic drift $c>0$, reflected at 0: \[Q_X^{(c)}(t)=\sup_{-\infty
1 citations