GTT (Groupe de Travail des Thésards) 18/10
schedule le lundi 18 octobre 2021 de 17h00 à 18h00
Organisé par : Arnould, Carrand, Ducrot, Khanfir, Marandon-Carlhian, Ocello
Intervenant : Miguel Martinez Herrera + Loïc Bethencourt (LPSM)
Lieu : Jussieu Salle Paul Lévy 16-26 209
Sujet : GTT (Groupe de Travail des Thésards)
Inference and tests for Multivariate Hawkes processes with Inhibition, application to neuroscience and genomics (Miguel MARTINEZ HERRERA)
Since its origin for the study of earthquakes, the Hawkes process models interactions interactions where the occurrence of an event has a direct impact on the phenomenon itself. The well-studied "excitation" increases the event rate each time we observe a point whereas the "inhibition", which is the main interest of this subject, considers the opposite effect. The main goal is to obtain a parametric estimation method for multidimensional processes, for which it is important to consider both probabilistic and statistical approaches. Such methods would provide a better understanding of the inner workings of interacting phenomena, such as neural activity networks.
Stable limit theorems for additive functionals of one-dimensional diffusion processes (Loïc BETHENCOURT)
We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some explicit conditions on the additive functional so that its fluctuations behave like some alpha-stable process in large time for alpha in(0,2].