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A Cluster Process Representation of a Self-Exciting Process

Alan G. Hawkes and David Oakes
Journal of Applied Probability
Vol. 11, No. 3 (Sep., 1974), pp. 493-503
DOI: 10.2307/3212693
Stable URL: http://www.jstor.org/stable/3212693
Page Count: 11
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A Cluster Process Representation of a Self-Exciting Process
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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.

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