A cluster process representation of a self-exciting process-Reference-Cited by-同舟云学术

A cluster process representation of a self-exciting process

Published:1974-09 Issue:3 Volume:11 Page:493-503
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:Journal of Applied Probability

Author:

Hawkes Alan G.,Oakes David

Abstract

It is shown that all stationary self-exciting point processes with finite intensity may be represented as Poisson cluster processes which are age-dependent immigration-birth processes, and their existence is established. This result is used to derive some counting and interval properties of these processes using the probability generating functional.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference14 articles.

1. Stochastic processes and population growth;Kendall;J. R. Statist. Soc.,1949

2. Point spectra of some mutually exciting point processes;Hawkes;J. R. Statist. Soc.,1971b

3. Spectra of some self-exciting and mutually exciting point processes

4. Daley D. J. and Vere-Jones D. (1971) A summary of the theory of point processes. Paper presented to the stochastic point process conference, New York, 1971.

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