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On the first passage time and leapover properties of Lévy motions

Author

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

Abstract

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.

Suggested Citation

  • Koren, T. & Chechkin, A.V. & Klafter, J., 2007. "On the first passage time and leapover properties of Lévy motions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(1), pages 10-22.
    • Handle: RePEc:eee:phsmap:v:379:y:2007:i:1:p:10-22
    DOI: 10.1016/j.physa.2006.12.039
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    Cited by:

    1. Vygintas Gontis, 2021. "Order flow in the financial markets from the perspective of the Fractional L\'evy stable motion," Papers 2105.02057, arXiv.org, revised Nov 2021.
    2. Wang, Xiao & Duan, Jinqiao & Li, Xiaofan & Song, Renming, 2018. "Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 618-634.
    3. Wijesundera, Isuri & Halgamuge, Malka N. & Nirmalathas, Ampalavanapillai & Nanayakkara, Thrishantha, 2016. "MFPT calculation for random walks in inhomogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 986-1002.

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