Demonstrates the representation of self-exciting point processes as Poisson cluster processes, indicating new insights into their properties.
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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Hawkes et al. (1974) studied this question.
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