TY - JOUR
T1 - Leapover lengths and first passage timet statistics for lévy flights
AU - Koren, Tal
AU - Lomholt, Michael A.
AU - Chechkin, Aleksei V.
AU - Klafter, Joseph
AU - Metzler, Ralf
PY - 2007/10/19
Y1 - 2007/10/19
N2 - 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 α are shown to have leapover lengths that are asymptotically power law distributed with an index α for one-sided LFs and, surprisingly, with an index α/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.
AB - 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 α are shown to have leapover lengths that are asymptotically power law distributed with an index α for one-sided LFs and, surprisingly, with an index α/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.
UR - http://www.scopus.com/inward/record.url?scp=35348959415&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.99.160602
DO - 10.1103/PhysRevLett.99.160602
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AN - SCOPUS:35348959415
SN - 0031-9007
VL - 99
JO - Physical Review Letters
JF - Physical Review Letters
IS - 16
M1 - 160602
ER -