First passage and first hitting times of Levy flights and Levy walks
First passage and first hitting times of Levy flights and Levy walks
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DOI：
10.1088/1367-2630/ab41bb
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发表时间：
2019-10-01
影响因子：
3.3
通讯作者：
Chechkin, Aleksei V.
中科院分区：
文献类型：
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作者：
Palyulin, Vladimir V.;Blackburn, George;Chechkin, Aleksei V.
对于 Levy 飞行和 Levy 步行搜索过程，我们分析了首次通过和首次命中（或首次到达）时间的完整分布。这些分别是粒子第一次移动穿过距其初始位置某个给定距离的点的时间，或第一次落在给定点的时间。对于列维运动来说，由于它们倾向于进行长重定位事件，因此有可能跳过空间中的给定点而不实际击中它（“跳跃”），这两个定义会导致显着不同的结果。我们研究了作为 Levy 稳定指数函数的首次通过和首次命中时间分布，突出了跳跃长度分布的第一个绝对矩为有限或无限时的不同行为。我们特别检查短时间和长时间的限制。我们的结果将应用于随机搜索过程的数学建模以及计算机算法。
For both Levy flight and Levy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Levy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Levy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.