Séminaire de Probabilités et Statistique :

Le 14 décembre 2015 à 15:00 - UM - Bât 09 - Salle de conférence (1er étage)

Présentée par Löcherbach Eva - Université de Cergy-Pontoise

On oscillating systems of interacting neurons.

We consider multi class systems of interacting nonlinear Hawkes processes modeling several large families of neurons. We prove propagation of chaos for such systems and associated central limit theorems. Moreover, we discuss situations in which the limit system exhibits oscillatory behavior. Finally, we show how these results can be related to certain PDMP's (piecewise deterministic Markov processes) and the study of their longtime behavior. This is a joint work with Susanne Ditlevsen.