An approximate formula for the first-crossing-time density of a Wiener process perturbed by
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In this paper, we develop a Monte Carlo based algorithm for estimating the FPT (first
passage time) density of the solution of a one-dimensional time-homogeneous SDE …

We consider a stochastic neuronal model in which the time evolution of the membrane
potential is described by a Wiener process perturbed by random jumps driven by a counting …

A standard convergence analysis of the simulation schemes for the hitting times of diffusions
typically requires non-degeneracy of their coefficients on the boundary, which excludes the …

The first passage time density of a diffusion process to a time varying threshold is of primary
interest in different fields. Here we consider a Brownian motion in presence of an …

For a non-singular Gaussian discrete-time series, the evaluation of the first passage time
probability distribution through a bounded time-varying boundary is considered by using …

Die vorliegende Arbeit ist motiviert durch biologische Fragestellungen bezüglich des
Verhaltens von Membranpotentialen in Neuronen. Ein vielfach betrachtetes Modell für …

In this thesis, we consider computational methods of finding exit probabilities for a class of
multivariate stochastic processes. While there is an abundance of results for one …

Abstract The Ornstein-Uhlenbeck neuronal model is investigated under the assumption that
the amplitude of the noise depends functionally on the signal. This assumption is deduced …

Abstract The University of Manchester: Hasan Mohammed O Alzubaidi: Doctor of
Philosophy: Numerical simulations of the spiking activity and the related rst exittime of …