nLab Hawkes process

Idea

In probability theory, a Hawkes process $(N_t)$ is a self-exciting point process with stochastic intensity

$$\lambda_t \;=\; \mu + \int_0^t \varphi (t-s) \mathrm{d} N_s \,,$$

where $\mu \geq 0$, and $\varphi \colon \mathbb{R}_+ \to \mathbb{R}_+$.

References

• Alan G. Hawkes, David Oakes: A Cluster Process Representation of a Self-Exciting Process, Journal of Applied Probability 11 3 (1974) 493-503 [doi:10.2307/3212693]

See also:

• Wikipedia: Hawkes Process