105 citations · 283 across the 22 of their papers we have counts for
4 papers · 1 filter
Hawkes processes with variable length memory and an infinite number of components
Pierre Hodara, Eva Löcherbach
In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of…
On a toy model of interacting neurons
Nicolas Fournier, Eva Löcherbach
We continue the study of a stochastic system of interacting neurons introduced in De Masi-Galves-Löcherbach-Presutti (2014). The system consists of N neurons, each spiking randomly…
Strongly degenerate time inhomogeneous SDEs: densities and support properties. Application to a Hodgkin-Huxley system with periodic input
Reinhard Höpfner, E. Löcherbach, M. Thieullen
In this paper we study the existence of densities for strongly degenerate stochastic differential equations (SDEs) whose coefficients depend on time and are not globally Lipschitz.…
Hydrodynamic limit for interacting neurons
Anna De Masi, Antonio Galves, Eva Löcherbach +1
This paper studies the hydrodynamic limit of a stochastic process describing the time evolution of a system with N neurons with mean-field interactions produced both by chemical an…