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

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1974 

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Footnotes

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

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