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 …

Stochastic differential equations play an increasingly important role in modeling the
dynamics of a large variety of systems in the natural sciences, and in technological …

A new computationally simple, speedy and accurate method is proposed to construct first-
passage-time probability density functions for Gauss–Markov processes through time …

Wang and Pötzelberger (1997) derived an explicit formula for the probability that a Brownian
motion crosses a one-sided piecewise linear boundary and used this formula to …

Using the Girsanov transformation we derive estimates for the accuracy of piecewise
approximations for one-sided and two-sided boundary crossing probabilities. We …

Diffusion processes have been extensively used to describe membrane potential behavior.
In this approach the interspike interval has a theoretical counterpart in the first-passage-time …

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 …

We give explicit upper bounds for convergence rates when approximating both one-and two-
sided general curvilinear boundary crossing probabilities for the Wiener process by similar …

Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-
looking problem of vast practical importance in physics, biology, chemistry, neuroscience …

Improved simulation schemes for the evaluation of first passage times through boundaries
for one dimensional diffusion processes can be obtained taking into account possible …