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Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
Boston University.
2008 (English)In: In and Out of Equilibrium 2 / [ed] Vladas Sidoravicius, Maria Eulalia Vares, Basel: Birkhäuser Verlag, 2008, Vol. 60, 383-427 p.Chapter in book (Refereed)
Abstract [en]

It has become common practice to use heavy-tailed distributions in order to describe the variations in time and space of network traffic workloads. The asymptotic behavior of these workloads is complex; different limit processes emerge depending on the specifies of the work arrival structure and the nature of the asymptotic scaling. We focus on two variants of the infinite source Poisson model and provide a coherent and unified presentation of the scaling theory by using integral representations. This allows us to understand physically why the various limit processes arise.

Place, publisher, year, edition, pages
Basel: Birkhäuser Verlag, 2008. Vol. 60, 383-427 p.
, Progress in Probability, 60
Keyword [en]
computer traffic, self-similar processes, fractional Brownian motion, stable processes, Poisson point processes, heavy tails, limit theorems
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
URN: urn:nbn:se:uu:diva-214079DOI: 978-3-7643-8786-0ISBN: 978-3-7463-8785-3OAI: oai:DiVA.org:uu-214079DiVA: diva2:683967
Available from: 2014-01-07 Created: 2014-01-07 Last updated: 2014-01-07

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