École Nationale Supérieure de
Techniques Avancées

Abstract

Many data are presented in the form of events that have a specific date and a variable (either discrete, indicating the type of event, or continuous, describing a quantity related to the event) called a mark. These data can be represented by what is called a marked point process. A point process is defined as a locally finite random measure on a subset E of a Euclidean space. This measure counts the random number of points falling within a bounded subset A included in E. If E = R × X, we call the point process a marked one, where R is the times axis and X the marks space. We focus on doing a review of modeling and statistical inference for Hawkes processes as a type of marked point process, using the maximisation of log-likelihood. We then move to Performing statistical inference for Hawkes models with nonexponential triggering function using the same log-likelihood approach.