3 citations · 9 across the 6 of their papers we have counts for
8 papers
Theoretical analysis and simulation methods for Hawkes processes and their diffusion approximation
Julien Chevallier, Anna Melnykova, Irene Tubikanec
Oscillatory systems of interacting Hawkes processes with Erlang memory kernels were introduced in Ditlevsen (2017). They are piecewise deterministic Markov processes (PDMP) and can…
Fluctuations for Spatially Extended Hawkes Processes
Julien Chevallier, Guilherme Ost
In a previous paper, it has been shown that the mean-field limit of spatially extended Hawkes processes is characterized as the unique solution of a neural field equation…
Uniform decomposition of probability measures: quantization, classification, rate of convergence
Julien Chevallier
The study of finite approximations of probability measures has a long history. In (Xu and Berger, 2017), the authors focus on constrained finite approximations and, in particular,…
Stimulus sensitivity of a spiking neural network model
Julien Chevallier
Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes…
Fluctuations for mean-field interacting age-dependent Hawkes processes
Julien Chevallier
The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +) being gran…
Mean-field limit of generalized Hawkes processes
Julien Chevallier
We generalize multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point. Within this class, we inve…
Microscopic approach of a time elapsed neural model
Julien Chevallier, Maria J. Caceres, Marie Doumic +1
The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And mor…
Detection of dependence patterns with delay
Julien Chevallier, Thomas Laloë
The Unitary Events (UE) method is a popular and efficient method used this last decade to detect dependence patterns of joint spike activity among simultaneously recorded neurons.…