Bottom-up models of functionally relevant patterns of neural activity provide an explicit link
between neuronal dynamics and computation. A prime example of functional activity …

We study a multivariate, non-linear Hawkes process ZN on the complete graph with N
nodes. Each vertex is either excitatory (probability p) or inhibitory (probability 1− p). We take …

We prove the existence of global-in-time regular solutions to a system of stochastic quadratic
reaction-diffusion equations. Global-in-time existence is based on a $ L^\infty $-estimate …

We consider a population of Hawkes processes modeling the activity of N interacting
neurons. The neurons are regularly positioned on the segment [0, 1], and the connectivity …

We study the convergence of N-particle systems described by SDEs driven by Brownian
motion and Poisson random measure, where the coefficients depend on the empirical …

These lecture notes present new results on statistical model selection for stochastic systems.
The majority of the results are original and first appeared in several recent papers co …

We prove a Large Deviation Principle for Hawkes Processes on sparse large disordered
networks with a graphon structure. We apply our results to a stochastic SIS epidemiological …

We consider a population of Hawkes processes modeling the activity of N interacting
neurons. The neurons are regularly positioned on the circle [− π, π], and the connectivity …

-Jusqu'ici je n'ai guère eu le choix.-C'est vrai. Eh bien moi, je vous propose un choix. Vous
connaissez le jeu de Pile ou Face? Je vous laisse choisir: Pile vous allez dans un sens, et …

We prove the existence of global-in-time regular solutions to a system of stochastic quadratic
reaction-diffusion equations. Global-in-time existence is based on a $ L^\infty $-estimate …