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Ratios of ordered points of point processes with regularly varying intensity measures

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Ipsen, Yuguang; Maller, Ross; Resnick, Sidney I.

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We study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to “large-trimming” properties of extremal processes and a variety of applications. Our point process approach facilitates a connection with the negative binomial process of Gregoire (1984) and consequently to certain generalised versions of the Poisson–Dirichlet distribution.

dc.contributor.authorIpsen, Yuguang
dc.contributor.authorMaller, Ross
dc.contributor.authorResnick, Sidney I.
dc.date.accessioned2021-01-25T04:44:38Z
dc.identifier.issn0304-4149
dc.identifier.urihttp://hdl.handle.net/1885/220003
dc.description.abstractWe study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to “large-trimming” properties of extremal processes and a variety of applications. Our point process approach facilitates a connection with the negative binomial process of Gregoire (1984) and consequently to certain generalised versions of the Poisson–Dirichlet distribution.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherElsevier
dc.rights© 2018 Elsevier B.V. All rights reserved.
dc.sourceStochastic Processes and their Applications
dc.subjectRegular variation
dc.subjectPoisson points
dc.subjectLévy process
dc.subjectNegative binomial
dc.subjectTrimming
dc.subjectOrder statistics
dc.titleRatios of ordered points of point processes with regularly varying intensity measures
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume129
dc.date.issued2019
local.identifier.absfor010404 - Probability Theory
local.identifier.ariespublicationu3102795xPUB257
local.publisher.urlhttps://www.sciencedirect.com/science/article/pii/S0304414918300401?via%3Dihub
local.type.statusPublished Version
local.contributor.affiliationIpsen, Yuguang, College of Business and Economics, ANU
local.contributor.affiliationMaller, Ross, College of Business and Economics, ANU
local.contributor.affiliationResnick, Sidney I., Cornell University
local.description.embargo2099-12-31
dc.relationhttp://purl.org/au-research/grants/arc/DP1092502
dc.relationhttp://purl.org/au-research/grants/arc/DP160103037
dc.relationhttp://purl.org/au-research/grants/arc/DP160103037
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage205
local.bibliographicCitation.lastpage222
local.identifier.doi10.1016/j.spa.2018.02.015
dc.date.updated2020-11-02T04:22:30Z
local.identifier.scopusID2-s2.0-85044110133
CollectionsANU Research Publications

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