105 citations · 283 across the 22 of their papers we have counts for
4 papers · 1 filter
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…
On the mathematical consequences of binning spike trains
B. Cessac, A. Le Ny, E. Loecherbach
We initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov pro…
Non-parametric estimation of the spiking rate in systems of interacting neurons
Pierre Hodara, Nathalie Krell, Eva Löcherbach
We consider a model of interacting neurons where the membrane potentials of the neurons are described by a multidimensional piecewise deterministic Markov process (PDMP) with value…
Estimating the interaction graph of stochastic neural dynamics
A. Duarte, A. Galves, E. Löcherbach +1
In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting cha…