Small and large scale behavior of moments of Poisson cluster processes

Antunes, N; Pipiras, V; Abry, P; Veitch, D

Small and large scale behavior of moments of Poisson cluster processes

Antunes, N Pipiras, V Abry, P Veitch, D

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Publication Type:: Journal Article
Citation:: ESAIM - Probability and Statistics, 2017, 21 pp. 369 - 393
Issue Date:: 2017-01-01

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Field	Value	Language
dc.contributor.author	Antunes, N	en_US
dc.contributor.author	Pipiras, V	en_US
dc.contributor.author	Abry, P	en_US
dc.contributor.author	Veitch, D https://orcid.org/0000-0001-8163-3464	en_US
dc.date.issued	2017-01-01	en_US
dc.identifier.citation	ESAIM - Probability and Statistics, 2017, 21 pp. 369 - 393	en_US
dc.identifier.issn	1292-8100	en_US
dc.identifier.uri	http://hdl.handle.net/10453/122334
dc.description.abstract	© EDP Sciences, SMAI. Poisson cluster processes are special point processes that find use in modeling Internet traffic, neural spike trains, computer failure times and other real-life phenomena. The focus of this work is on the various moments and cumulants of Poisson cluster processes, and specifically on their behavior at small and large scales. Under suitable assumptions motivated by the multiscale behavior of Internet traffic, it is shown that all these various quantities satisfy scale free (scaling) relations at both small and large scales. Only some of these relations turn out to carry information about salient model parameters of interest, and consequently can be used in the inference of the scaling behavior of Poisson cluster processes. At large scales, the derived results complement those available in the literature on the distributional convergence of normalized Poisson cluster processes, and also bring forward a more practical interpretation of the so-called slow and fast growth regimes. Finally, the results are applied to a real data trace from Internet traffic.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP120102834
dc.relation.ispartof	ESAIM - Probability and Statistics	en_US
dc.relation.isbasedon	10.1051/ps/2017018	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Small and large scale behavior of moments of Poisson cluster processes	en_US
dc.type	Journal Article
utslib.citation.volume	21	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0104 Statistics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - GBDTC - Global Big Data Technologies
utslib.copyright.status	open_access	*
pubs.publication-status	Published	en_US
pubs.volume	21	en_US

Abstract:

© EDP Sciences, SMAI. Poisson cluster processes are special point processes that find use in modeling Internet traffic, neural spike trains, computer failure times and other real-life phenomena. The focus of this work is on the various moments and cumulants of Poisson cluster processes, and specifically on their behavior at small and large scales. Under suitable assumptions motivated by the multiscale behavior of Internet traffic, it is shown that all these various quantities satisfy scale free (scaling) relations at both small and large scales. Only some of these relations turn out to carry information about salient model parameters of interest, and consequently can be used in the inference of the scaling behavior of Poisson cluster processes. At large scales, the derived results complement those available in the literature on the distributional convergence of normalized Poisson cluster processes, and also bring forward a more practical interpretation of the so-called slow and fast growth regimes. Finally, the results are applied to a real data trace from Internet traffic.

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http://hdl.handle.net/10453/122334