Spectra of Some Self-Exciting and Mutually Exciting Point Processes¶
HAWKES, A. G. (1971). Spectra of Some Self-Exciting and Mutually Exciting Point Processes. Biometrika, 58(1), 83-90.
Cited by¶
2 citations across 2 artifacts.
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Primes¶
- Poisson Process
- And reach, in order, for inhomogeneous Poisson when the rate varies smoothly, Cox / doubly-stochastic Poisson when the rate itself is stochastic, and Hawkes / self-exciting processes when an event raises the probability of the next.
This sourceIntroduces self-exciting (Hawkes) processes in which an event raises the probability of the next — the named departure for clustering/retry-storm dynamics.
- And reach, in order, for inhomogeneous Poisson when the rate varies smoothly, Cox / doubly-stochastic Poisson when the rate itself is stochastic, and Hawkes / self-exciting processes when an event raises the probability of the next.
Mechanisms¶
- Poisson Event Model
- Events frequently cluster — one outage triggers a burst of calls, one tremor triggers aftershocks — a self-exciting pattern the constant-rate Poisson cannot represent, and such data are typically overdispersed with variance far above the mean.
This sourceSelf-exciting point processes represent event clustering through history-dependent intensity, which a constant-rate Poisson process cannot express.
- Events frequently cluster — one outage triggers a burst of calls, one tremor triggers aftershocks — a self-exciting pattern the constant-rate Poisson cannot represent, and such data are typically overdispersed with variance far above the mean.
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