École Nationale Supérieure de
Techniques Avancées

Abstract

This report aims to model the occurrence of discrete events, such as earthquakes, using point processes, with a particular focus on the Hawkes process. A theoretical study was conducted, starting with the homogeneous and non-homogeneous Poisson processes, focusing on their properties and the estimation of conditional intensity parameters using the maximum likelihood method. Numerical simulations in Python were carried out to illustrate the trajectories of our processes and to validate certain theoretical results. Finally, we applied everything we studied to analyze Japanese seismic data, demonstrating the relevance of the Hawkes process in capturing the self-excitation phenomenon of earthquakes.