ABSTRACT

Seizures ..................................................................................................................... 213 13.2.3 Rationales for the Analogy between Earthquakes, Financial Crashes, and

Epileptic Seizures ..................................................................................................... 217 13.2.4 Generic Phase Diagram of Coupled Threshold Oscillators of Relaxation ............... 218

13.3 Self-Excited Hawkes Process for Epileptic Seizures ............................................................220 13.3.1 Particles versus Waves ..............................................................................................220 13.3.2 Brief Classi–cation of Point Processes ..................................................................... 221

13.3.2.1 Renewal Processes ..................................................................................... 222 13.3.2.2 Clustering Models ...................................................................................... 223 13.3.2.3 Self-Excited Models ...................................................................................224 13.3.2.4 Marked Self-Excited Point Processes ........................................................224