The first passage time on the (reflected) Brownian motion with broken drift hitting a random boundary

Zhenwen Zhao and Yuejuan Xi

Statistics & Probability Letters, 2021, vol. 171, issue C

Abstract: This paper studies the first passage times of a (reflected) Brownian motion with broken drift over a random boundary. The time-dependent Meyer–Tanaka formula allows us to obtain the formulas on the joint Laplace transform of the hitting time and hitting position. This paper extends the results of first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes in Perry et al. (2004).

Keywords: Broken drift; The first passage time; Laplace transform (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109040

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