A randomized first-passage problem for drifted Brownian motion subject to hold and jump from a boundary

Abstract

We study an inverse first-passage-time problem for Wiener process $X(t)$ subject to hold and jump from a boundary $c.$ Let be given a threshold $S>X(0)\ge c,$ and a distribution function $F$ on $[0,+\infty ).$ The problem consists in finding the distribution of the holding time at $c$ and the distribution of jumps from $c,$ so that the first-passage time of $X(t)$ through $S$ has distribution $F.$

References in corpus (2)

• On the inverse first-passage-time problem for a Wiener process
• One-dimensional reflected diffusions with two boundaries and an inverse first-hitting problem