Hawkes Branching Renewal Criticality
Follow expected event clusters through a self-exciting kernel and separate critical growth from stationarity.
Free theory articleFollow expected event clusters through a self-exciting kernel and separate critical growth from stationarity.
Concept & interpretation
The Hawkes process is a self-exciting point process where each event increases the likelihood of subsequent events. It can be viewed as a branching process with an exogenous immigration baseline rate μ and an expected descendant cluster size governed by the branching ratio η = α / β. It is essential to differentiate between the dynamics of a single exogenous seed at time 0 (with no further immigrants in its descendant cluster) and a continuous immigration process.
Experiment
Using the interactive module Hawkes Branching Renewal Criticality:
- Select a value for the Immigration baseline rate.
- Select the Kernel decay parameter to control how fast the excitation decays.
- Adjust the Branching ratio to see its effect on subcritical, critical, and supercritical regimes.
- Select the evaluation Time for transient observations.
- Set the Generations to compute the mass through generation G.