Perfect simulation of Hawkes processes

Jesper Møller; Jakob Gulddahl Rasmussen

doi:10.1239/aap/1127483739

Perfect simulation of Hawkes processes

Jesper Møller, Jakob Gulddahl Rasmussen

Institut for Matematiske Fag

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

56 Citationer (Scopus)

Abstract

Our objective is to construct a perfect simulation algorithm for unmarked and marked Hawkes processes. The usual straightforward simulation algorithm suffers from edge effects, whereas our perfect simulation algorithm does not. By viewing Hawkes processes as Poisson cluster processes and using their branching and conditional independence structures, useful approximations of the distribution function for the length of a cluster are derived. This is used to construct upper and lower processes for the perfect simulation algorithm. A tail-lightness condition turns out to be of importance for the applicability of the perfect simulation algorithm. Examples of applications and empirical results are presented.
Udgivelsesdato: SEP

Originalsprog	Engelsk
Tidsskrift	Advances in Applied Probability
Vol/bind	37
Udgave nummer	3
Sider (fra-til)	629-646
Antal sider	18
ISSN	0001-8678
DOI	https://doi.org/10.1239/aap/1127483739
Status	Udgivet - 2005

Emneord

Approximate simulation
Dominated coupling from the past
Poisson cluster process

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10.1239/aap/1127483739

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Citationsformater

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N2 - Our objective is to construct a perfect simulation algorithm for unmarked and marked Hawkes processes. The usual straightforward simulation algorithm suffers from edge effects, whereas our perfect simulation algorithm does not. By viewing Hawkes processes as Poisson cluster processes and using their branching and conditional independence structures, useful approximations of the distribution function for the length of a cluster are derived. This is used to construct upper and lower processes for the perfect simulation algorithm. A tail-lightness condition turns out to be of importance for the applicability of the perfect simulation algorithm. Examples of applications and empirical results are presented.

AB - Our objective is to construct a perfect simulation algorithm for unmarked and marked Hawkes processes. The usual straightforward simulation algorithm suffers from edge effects, whereas our perfect simulation algorithm does not. By viewing Hawkes processes as Poisson cluster processes and using their branching and conditional independence structures, useful approximations of the distribution function for the length of a cluster are derived. This is used to construct upper and lower processes for the perfect simulation algorithm. A tail-lightness condition turns out to be of importance for the applicability of the perfect simulation algorithm. Examples of applications and empirical results are presented.

KW - Approximate simulation

KW - Dominated coupling from the past

KW - Poisson cluster process

KW - Approximate simulation

KW - Dominated coupling from the past

KW - Poisson cluster process

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DO - 10.1239/aap/1127483739

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EP - 646

JO - Advances in Applied Probability

JF - Advances in Applied Probability

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ER -

Perfect simulation of Hawkes processes

Abstract

Emneord

Adgang til dokumentet

AUB Link

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