This article presents a mini-review about the progress in inferring monosynaptic connections
from spike trains of multiple neurons over the past twenty years. First, we explain a variety of …

We consider the problem of computing the survival (first-passage) probability density
function of jump-diffusion models with two stochastic factors. In particular the Fokker–Planck …

Background Parkinson's disease (PD) is a neurodegenerative disease characterized by
tremor, stiffness, and slowness of movement. Many studies showed an abnormality of …

We develop a method from semiparametric statistics (Cox, 1972) for the purpose of tracking
links and connection strengths over time in a neuronal network from spike train data. We …

Given a two-dimensional correlated diffusion process, we determine the joint density of the
first passage times of the process to some constant boundaries. This quantity depends on …

Concurrent measurements of neural activity at multiple scales, sometimes performed with
multimodal techniques, become increasingly important for studying brain function. However …

With the aim to describe the interaction between a couple of neurons a stochastic model is
proposed and formalized. In such a model, maintaining statements of the Leaky Integrate …

This paper investigates the probabilistic properties that determine the existence of space-
time transformations between diffusion processes. We prove that two diffusions are related …

Recent technological advances, which allow for simultaneous recording of spikes and local
field potentials (LFPs) at multiple sites in a given cortical area or across different areas, have …

We consider a bivariate Gauss–Markov process and we study the first passage time of one
component through a constant boundary. We prove that its probability density function is the …