Interacting Hawkes processes with multiplicative inhibition

16.02.2022, 10:00  –  Online (Zoom)
Forschungsseminar Statistik

Celine Duval (Université de Paris)

Abstract: After a shot introduction on Hawkes processes, we introduce a general class of mean-field interacting nonlinear Hawkes processes modelling the reciprocal interactions between two neuronal populations, one excitatory and one inhibitory. The model incorporates two features: inhibition, which acts as a multiplicative factor onto the intensity of the excitatory population and additive retroaction from the excitatory neurons onto the inhibitory ones. We detail the well-posedness of this interacting system as well as its dynamics in large population. The analysis of the longtime behavior of the mean-field limit process can be explicated. We illustrate numerically that inhibition and retroaction may be responsible for the emergence of limit cycles. (j.w. with E. Luçon and C. Pouzat)

Zoom link can be found here: www.wias-berlin.de/research/rgs/fg6/mathsem.jsp