nLab Hawkes process

Contents

Idea

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

λ t=μ+ 0 tφ(ts)dN s, \lambda_t \;=\; \mu + \int_0^t \varphi (t-s) \mathrm{d} N_s \,,

where μ0\mu \geq 0, and φ: + +\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:

Last revised on March 19, 2025 at 21:28:30. See the history of this page for a list of all contributions to it.