Leapover lengths and first passage time statistics for Lévy flights.
Exact results for the first passage time and leapover statistics of symmetric and one-sided Lévy flights (LFs) are derived. LFs with a stable index alpha are shown to have leapover lengths that are asymptotically power law distributed with an index alpha for one-sided LFs and, surprisingly, with an index alpha/2 for symmetric LFs. The first passage time distribution scales like a power law with an index 1/2 as required by the Sparre-Andersen theorem for symmetric LFs, whereas one-sided LFs have a narrow distribution of first passage times. The exact analytic results are confirmed by extensive simulations.
Koren
Tal
T
School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel.
Lomholt
Michael A
MA
Chechkin
Aleksei V
AV
Klafter
Joseph
J
Metzler
Ralf
R