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


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.

Research Papers
Copyright © Applied Probability Trust 1974 

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


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