Estimation of the Memory Parameter of the Infinite Source Poisson Process

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dc.creatorFay, Gilles
dc.creatorRoueff, François
dc.creatorSoulier, Philippe
dc.date2005-09-16
dc.date2007-10-01
dc.date.accessioned2026-07-07T08:32:58Z
dc.date.available2026-07-07T08:32:58Z
dc.descriptionLong-range dependence induced by heavy tails is a widely reported feature of internet traffic. Long-range dependence can be defined as the regular variation of the variance of the integrated process, and half the index of regular variation is then referred to as the Hurst index. The infinite-source Poisson process (a particular case of which is the $M/G/\infty$ queue) is a simple and popular model with this property, when the tail of the service time distribution is regularly varying. The Hurst index of the infinite-source Poisson process is then related to the index of regular variation of the service times. In this paper, we present a wavelet-based estimator of the Hurst index of this process, when it is observed either continuously or discretely over an increasing time interval. Our estimator is shown to be consistent and robust to some form of non-stationarity. Its rate of convergence is investigated.
dc.descriptionFinal version
dc.identifierhttps://arxiv.org/abs/math/0509371
dc.identifierhttp://arxiv.org/abs/math/0509371
dc.identifierThe Bernoulli Society / IMS Journal "Bernoulli" 13, 2 (2007) 473--491
dc.identifierdoi:10.3150/07-BEJ5123
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138970
dc.subjectStatistics Theory
dc.subject62M09 (Primary); 60K25 (Secondary)
dc.titleEstimation of the Memory Parameter of the Infinite Source Poisson Process
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