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A cluster process representation of a self-exciting process

Published online by Cambridge University Press:  14 July 2016

Alan G. Hawkes  and
David Oakes
Alan G. Hawkes*
Affiliation:
University of Durham
David Oakes*
Affiliation:
Imperial College London
*
* Now at University College Swarsea.
** Now at Harvard University.
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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.

Keywords

CLUSTER PROCESSPOINT PROCESSSELF-EXCITING PROCESS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 493 - 503
Copyright
Copyright © Applied Probability Trust 1974 

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Footnotes

Supported by the Science Research Council and N. S. F. grant GS32327X.

References

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