29 citations · 59 across the 7 of their papers we have counts for
4 papers · 1 filter
Mean field limits for nonlinear spatially extended hawkes processes with exponential memory kernels
Julien Chevallier, A Duarte, E Löcherbach +1
We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in Rd and study the associated mean field limits. As the t…
Stability, convergence to equilibrium and simulation of non-linear Hawkes Processes with memory kernels given by the sum of Erlang kernels
Aline Duarte, Eva Löcherbach, Guilherme Ost
Non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels are considered. It is shown that their stability properties can be studied in terms of an associa…
Hydrodynamic Limits for Spatially Structured Interacting Neurons
Aline Duarte, Guilherme Ost, Andrés Rodríguez
In this paper we study the hydrodynamic limit for a stochastic process describing the time evolution of the membrane potentials of a system of neurons with spatial dependency. We d…
A model for neural activity in the absence of external stimuli
Aline Duarte, Guilherme Ost
We study a stochastic process describing the continuous time evolution of the membrane potentials of finite system of neurons in the absence of external stimuli. The values of the…