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 …

A large class of statistical decision models for performance in simple information processing
tasks can be described by linear, first-order, stochastic differential equations (SDEs), whose …

A detailed study of the asymptotic behavior of the first-passage-time pdf and its moments is
carried out for an unrestricted conditional Ornstein-Uhlenbeck process and for a constant …

Visual psychophysics has shown that the perceptual representation of a stimulus has
complex time-varying properties that depend on the response characteristics of the channel …

The first-passage-time pdf through a time-dependent boundary for one-dimensional
diffusion processes is proved to satisfy a new Volterra integral equation of the second kind …

A stochastic diffusion model related to a reformulation of the Richards growth curve is
proposed. The main characteristics of the process are studied, and the problem of maximum …

The stochastic neuronal model with reversal potentials is approximated. For the model with
constant postsynaptic potential amplitudes, a deterministic approximation is the only one …

The asymptotic behaviour of the first-passage-time pdf through a constant boundary for an
Ornstein–Uhlenbeck process is investigated for large boundaries. It is shown that an …

Stein's model represents a commonly-used description of spontaneous neuronal activity.
Substituting Stein's model by the Ornstein-Uhlenbeck diffusion process increases the model …

We prove that for a diffusion process the first-passage-time pdf through a continuous-time
function with bounded derivative satisfies a Volterra integral equation of the second kind …