On the first passage time and leapover properties of Lévy motions

T. Koren*, A. V. Chechkin, J. Klafter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We investigate two coupled properties of Lévy stable random motions: the first passage times (FPTs) and the first passage leapovers (FPLs). While, in general, the FPT problem has been studied quite extensively, the FPL problem has hardly attracted any attention. Considering a particle that starts at the origin and performs random jumps with independent increments chosen from a Lévy stable probability law λα,β(x), the FPT measures how long it takes the particle to arrive at or cross a target. The FPL addresses a different question: given that the first passage jump crosses the target, then how far does it get beyond the target? These two properties are investigated for three subclasses of Lévy stable motions: (i) symmetric Lévy motions characterized by Lévy index α(0<α<2) and skewness parameter β=0, (ii) one-sided Lévy motions with 0<α<1, β=1, and (iii) two-sided skewed Lévy motions, the extreme case, 1<α<2, β=-1.

Original languageEnglish
Pages (from-to)10-22
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
StatePublished - 1 Jun 2007


FundersFunder number
Deutsche ForschungsgemeinschaftHa 1517/26-1,2


    • Brownian motion
    • First passage time
    • Leapover
    • Lévy motion
    • Lévy stable distributions


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