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摘要翻译：
给出了对称和单边Levy飞行(LFs)的第一次通过时间和跳跃统计量的精确结果。具有稳定指数α的LFs具有跳跃长度，对于单侧LFs，其跳跃长度随指数α呈渐近幂律分布，而对于对称LFs，其跳跃长度随指数α/2呈渐近幂律分布。对称LFs的首次通过时间分布类似于指数为1/2的幂律，而单边LFs的首次通过时间分布很窄。通过大量的仿真验证了精确的分析结果。
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英文标题：
《Leapover lengths and first passage time statistics for L\'evy flights》
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作者：
Tal Koren, Michael A. Lomholt, Aleksei V. Chechkin, Joseph Klafter,
Ralf Metzler
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/706.3641
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