On the first passage of one-sided Lévy motions

Iddo Eliazar and Joseph Klafter

Physica A: Statistical Mechanics and its Applications, 2004, vol. 336, issue 3, 219-244

Abstract: We study the first passage problem for one-sided Lévy motions: how does such a motion, started at the origin, cross a barrier positioned at the point x (x>0)? Since one-sided Lévy motions are pure-jump processes, they always ‘leap’ over barriers (rather than crossing them continuously). We hence explore the following issues: (i) first passage times (FPTs)—how long would it take the motion to cross the barrier; (ii) first passage leapovers (FPLs)—how far would the motion leap over the barrier; and, (iii) what is dependence between the FPTs and the FPLs.

Keywords: One-sided Lévy motions; Heavy-tailed Lévy motions; Self-similar Lévy motions; First passage times; First passage leapovers; Scaling limits; Mittag–Leffler probability laws; Fisher probability laws (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:336:y:2004:i:3:p:219-244

DOI: 10.1016/j.physa.2003.12.032

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