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First passage and first hitting times of Lévy flights and Lévy walks
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Palyulin, Vladimir V., Blackburn, George, Lomholt, Michael A., Watkins, Nicholas W., Metzler, Ralf, Klages, Rainer and Chechkin, Aleksei V. (2019) First passage and first hitting times of Lévy flights and Lévy walks. New Journal of Physics, 21 (10). 103028. doi:10.1088/1367-2630/ab41bb ISSN 1367-2630.
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Official URL: http://dx.doi.org/10.1088/1367-2630/ab41bb
Abstract
For both Lévy flight and Lévy 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 Lévy 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 Lévy 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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Physics | ||||
Library of Congress Subject Headings (LCSH): | Statistical mechanics, Lévy processes, Probabilities, Fractals, Random walks (Mathematics) | ||||
Journal or Publication Title: | New Journal of Physics | ||||
Publisher: | IOP Publishing | ||||
ISSN: | 1367-2630 | ||||
Official Date: | 2019 | ||||
Dates: |
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Volume: | 21 | ||||
Number: | 10 | ||||
Article Number: | 103028 | ||||
DOI: | 10.1088/1367-2630/ab41bb | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 12 November 2019 | ||||
Date of first compliant Open Access: | 18 November 2019 |
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