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Convergence to fractional Brownian motion and to the telecom process: the integral representation approach. (English) Zbl 1154.60020
Sidoravicius, Vladas (ed.) et al., In and out of equilibrium 2. Papers celebrating the 10th edition of the Brazilian school of probability (EBP), Rio de Janiero, Brazil, July 30 to August 4, 2006. Basel: Birkhäuser (ISBN 978-3-7643-8785-3/hbk). Progress in Probability 60, 383-427 (2008).
Authors’ abstract: 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 specifics 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.
For the entire collection see [Zbl 1141.82002].

60F05 Central limit and other weak theorems
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60G18 Self-similar stochastic processes
60G52 Stable stochastic processes