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A cluster process representation of a self-exciting process

  • Alan G. Hawkes (a1) and David Oakes (a2)

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.

Corresponding author
* Now at University College Swarsea.
** Now at Harvard University.
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Supported by the Science Research Council and N. S. F. grant GS32327X.

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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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