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 …

The first-crossing-time problem through two time-dependent boundaries for one-
dimensional diffusion processes is considered. The first-crossing pdf's from below and from …

Making use of the integral equations given in [1],[2] and [3], the asymptotic behaviour of the
first-passage time (FPT) pdf's through certain time-varying boundaries, including periodic …

Explicit formulae are found for the probability that the Brownian motion, Bt, up-crosses, in [0,
T], a piecewise-linear function S (t), with the condition that the value of Bt is assigned at a …

Some problems of first-crossing times over two time-dependent boundaries for one-
dimensional jump-diffusion processes are considered. The moments of the first-crossing …

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 …

A special class of time-inhomogeneous diffusion processes, generated starting from Gauss–
Markov processes conditioned on the same initial state, is considered. This class includes …

We consider a bilateral birth-death process having sigmoidal-type rates. A thorough
discussion on its transient behaviour is given, which includes studying symmetry properties …

The first-passage time τ S (x) of a one-dimensional continuous stochastic process X (t),
starting from x≤ S (0), through a smooth boundary S (t) is investigated; in particular …

One dimensional diffusion processes have been increasingly invoked to model a variety of
biological, physical and engineering systems subject to random fluctuations (cf., for instance …