Journal
NEW JOURNAL OF PHYSICS
Volume 21, Issue 10, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/ab41bb
Keywords
Levy flights; Levy walks; first-passage time; first-hitting time
Categories
Funding
- Deutsche Forschungsgemeinschaft [ME1535/6-1, ME1535/7-1]
- Alexander von Humboldt Honorary Research Scholarship from the Foundation for Polish Science
- ONR Global NICOP grant [N62909-15-1-N143]
- ONR Global
- London Mathematical Laboratory
- Deutsche Forschungsgemeinschaft (German Research Foundation)
- Open Access Publication Fund of Potsdam University
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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.
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