Perfect simulation of Hawkes processes

Perfect simulation of Hawkes processes

Jesper Møller and Jakob G. Rasmussen

Source: Adv. in Appl. Probab. Volume 37, Number 3 (2005), 629-646.

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.

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Primary Subjects: 60G55

Secondary Subjects: 68U20

Keywords: Approximate simulation; dominated coupling from the past; edge effect; exact simulation; marked Hawkes process; marked point process; perfect simulation; point process; Poisson cluster process; thinning; upper process; lower process

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aap/1127483739
Digital Object Identifier: doi:10.1239/aap/1127483739
Zentralblatt MATH identifier: 1074.60057
Mathematical Reviews number (MathSciNet): MR2156552

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