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On telegraph processes, their first passage times and running extrema

Nikita Ratanov ()

Statistics & Probability Letters, 2021, vol. 174, issue C

Abstract: In this note, we present some ideas for describing the distributions of the running maximum/minimum, first passage times and telegraphic meanders. Explicit formulae for joint distribution of the extrema, the number of velocity switches and the terminal position are derived using coupled integral equations technique.

Keywords: Asymmetric piecewise linear process; First passage time; Kac’s scaling; Coupled integral equations; Telegraphic meander; Running maximum (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109101

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