  Exact results for the first passage time and leapover statistics of symmetric
and one-sided Levy flights (LFs) are derived. LFs with stable index alpha are
shown to have leapover lengths, that are asymptotically power-law distributed
with index alpha for one-sided LFs and, surprisingly, with index alpha/2 for
symmetric LFs. The first passage time distribution scales like a power-law with
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.
