First passage times for some classes of fractional time-changed diffusions

A note on first-passage times of continuously time-changed Brownian motion

The probability of a Brownian motion with drift to remain between two constant barriers (for some period of time) is known explicitly. In mathematical finance, this and related results are required, e.g., for the pricing of singleand double-barrier options in a Black-Scholes framework. One popular possibility to generalize the Black-Scholes model is to introduce a stochastic time-scale. This eq...

First Passage Time Moments of Jump-Diffusions with Markovian Switching

On last passage times of linear diffusions to curved boundaries

The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following Robbins & Siegmund, we then show that this expression may be computed for some implicit boundaries via a martingale method. Finally, we discuss some links betw...

On first range times of linear diffusions

First passage times for a tracer particle in single file diffusion and fractional Brownian motion.

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-...