Estimating the input of a Lévy queue by Poisson sampling of the workload process
Oberseminar Darmstadt
Datum: 15.11.2018
Zeit: 16:15–17:45 Uhr
This paper aims at semi-parametrically estimating the input process to a Lévy-driven queue by sampling the workload process at Poisson times. We construct a method-of- moments based estimator for the Lévy process’ characteristic exponent. This method exploits the known distribution of the workload sampled at an exponential time, thus taking into account the dependence between subsequent samples. Verifiable conditions for consistency and asymptotic normality are provided, along with explicit expressions for the asymptotic variance. The method requires an intermediate estimation step of estimating a constant (related to both the input distribution and the sampling rate); this constant also features in the asymptotic analysis. For subordinator Lévy input, a partial MLE is constructed for the intermediate step and we show that it satisfies the consistency and asymptotic normality conditions. For general spectrally-positive Lévy input a biased estimator is proposed that only uses workload observations above some threshold; the bias can be made arbitrarily small by appropriately choosing the threshold.
Referent
- Dr. Liron Ravner, Universiteit Amsterdam
Ort
- TU Darmstadt S2|15 Raum 401
- Schlossgartenstr. 7, 64289 Darmstadt
Veranstalter
- Technische Universität Darmstadt
Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381
info(at)stochastik-rhein-mainde
Kooperationspartner
Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz