First passage and first hitting times of Levy flights and Levy walks
- 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.
Author details: | Vladimir V. PalyulinORCiD, George Blackburn, Michael A. LomholtORCiD, Nicholas W. WatkinsORCiD, Ralf MetzlerORCiDGND, Rainer KlagesORCiDGND, Aleksei ChechkinORCiDGND |
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DOI: | https://doi.org/10.1088/1367-2630/ab41bb |
ISSN: | 1367-2630 |
Title of parent work (English): | New journal of physics : the open-access journal for physics |
Publisher: | IOP Publ. Ltd. |
Place of publishing: | Bristol |
Publication type: | Article |
Language: | English |
Year of first publication: | 2019 |
Publication year: | 2019 |
Release date: | 2020/10/30 |
Tag: | Levy flights; Levy walks; first-hitting time; first-passage time |
Volume: | 21 |
Issue: | 10 |
Number of pages: | 23 |
Funding institution: | Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [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)German Research Foundation (DFG); Open Access Publication Fund of Potsdam University |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access |
Open Access / Gold Open-Access | |
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