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

Yuguang Ipsen; Ross Maller; Sidney Resnick

doi:10.1016/j.spa.2018.02.015

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

Yuguang Ipsen^*
, Ross Maller
, Sidney Resnick

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	205-222
Number of pages	18
Journal	Stochastic Processes and their Applications
Volume	129
Issue number	1
DOIs	https://doi.org/10.1016/j.spa.2018.02.015
Publication status	Published - Jan 2019

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title = "Ratios of ordered points of point processes with regularly varying intensity measures",

abstract = "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.",

keywords = "L{\'e}vy process, Negative binomial, Order statistics, Poisson points, Regular variation, Trimming",

author = "Yuguang Ipsen and Ross Maller and Sidney Resnick",

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year = "2019",

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AU - Ipsen, Yuguang

AU - Maller, Ross

AU - Resnick, Sidney

PY - 2019/1

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N2 - 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.

AB - 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.

KW - Lévy process

KW - Negative binomial

KW - Order statistics

KW - Poisson points

KW - Regular variation

KW - Trimming

UR - https://www.scopus.com/pages/publications/85044110133

U2 - 10.1016/j.spa.2018.02.015

DO - 10.1016/j.spa.2018.02.015

M3 - Article

SN - 0304-4149

VL - 129

SP - 205

EP - 222

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

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

Abstract

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