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arXiv · 1509.03448

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

Mario Abundo
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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 $F.$

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Mario Abundo. 2015-09-11. A randomized first-passage problem for drifted Brownian motion subject to hold and jump from a boundary. https://doi.org/10.1080/07362994.2015.1099047

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