Mathematical models are an important tool for neuroscientists. During the last 30 years
many papers have appeared on single neuron description and specifically on stochastic …

We consider multi-class systems of interacting nonlinear Hawkes processes modeling
several large families of neurons and study their mean field limits. As the total number of …

We continue the study of a stochastic system of interacting neurons introduced in De Masi,
Galves, Löcherbach and Presutti (J. Stat. Phys. 158 (2015) 866–902). The system consists of …

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 …

When spinal circuits generate rhythmic movements it is important that the neuronal activity
remains within stable bounds to avoid saturation and to preserve responsiveness. Here, we …

We show that the stochastic Morris–Lecar neuron, in a neighborhood of its stable point, can
be approximated by a two-dimensional Ornstein–Uhlenbeck (OU) modulation of a constant …

We consider the problem of efficient estimation of the drift parameter of an Ornstein–
Uhlenbeck type process driven by a Lévy process when high-frequency observations are …

Two diffusion processes with multiplicative noise, able to model the changes in the neuronal
membrane depolarization between two consecutive spikes of a single neuron, are …

Direct measurements of synaptic inhibition (I) and excitation (E) to spinal motoneurons can
provide an important insight into the organization of premotor networks. Such measurements …

Parameter estimation in multidimensional diffusion models with only one coordinate
observed is highly relevant in many biological applications, but a statistically difficult …