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 …

Abstract The Ornstein–Uhlenbeck process is presented with its main mathematical
properties and with original results on the first crossing times in the case of two threshold …

The stochastic Ornstein-Uhlenbeck neuronal model is studied, and estimators of the model
input parameters, depending on the firing regime of the process, are derived. Closed …

The Ornstein–Uhlenbeck neuronal model is investigated under the assumption that the
amplitude of the noise is signal dependent. A linear approximation of the input–output …

We propose an approach to compute the boundary crossing probabilities for a class of
diffusion processes which can be expressed as piecewise monotone (not necessarily one-to …

A reliable Monte Carlo method for the evaluation of first passage times of diffusion
processes through boundaries is proposed. A nested algorithm that simulates the first …

Weexplore a method for finding the State H (t) of a Stochastic System when the first exit time
or hitting time probability density function g (t) is given. The task is to find an analytic form for …

Since diffusion processes arise in so many different fields, efficient technics for the
simulation of sample paths, like discretization schemes, represent crucial tools in applied …

We consider a general one-dimensional diffusion process and we study the probability of
crossing a boundary for the associated pinned diffusion as the time at which the conditioning …

The distribution of time intervals between successive spikes generated by a neuronal cell–
the interspike intervals (ISI)–may reveal interesting features of the underlying dynamics. In …