The Hawkes process is a particular version of a point process that models phenomena that interact with each other. Originally, this model focused on self-exciting effects where the observation of one event increases the probability of another event occurring, such as earthquakes and their aftershocks. However, when observing certain phenomena such as the interaction between neurons in a brain, the opposite effect can also be observed: When one neuron is activated, it can inhibit other connected neurons, making them less likely to be activated. 

 

The main goal of the PhD is to study this type of interaction from a mathematical point of view. This would allow obtaining various results concerning the estimation of interaction graphs and parameters which can then be used to understand the inner workings of the studied phenomena. The second goal is to apply our results to the study of neuron interactions and the study of the replication origins of genomes. This PhD combines both theoretical and practical approaches with an emphasis on making all numerical results accessible.

 

PhD student: Miguel Alejandro Martinez Herrera

PhD supervisors: Anna Bonnet, Arnaud Guyader, Maxime Sangnier

Research laboratory: Laboratoire de Probabilités, Statistique et Modélisation