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

Mario Abundo

doi:10.1080/07362994.2015.1099047

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

Probability 2017-03-02 v1

Authors: 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 $F.$

Keywords

first-passage time Brownian motion inverse first-passage problem boundary holding boundary jumping distribution function holding time

Cite

@article{arxiv.1509.03448,
  title  = {A randomized first-passage problem for drifted Brownian motion subject to hold and jump from a boundary},
  author = {Mario Abundo},
  journal= {arXiv preprint arXiv:1509.03448},
  year   = {2017}
}

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