1 citations · 2 across the 2 of their papers we have counts for
4 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,…
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…