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First passage and first hitting times of Lévy flights and Lévy walks

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), article no. 103028.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1088/1367-2630/ab41bb
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Abstract

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 Item
Copyright Holders: 2019 The Authors
ISSN: 1367-2630
Keywords: Paper, Lévy flights, Lévy walks, first-passage time, first-hitting time
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Engineering and Innovation
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 67266
SWORD Depositor: Jisc Publications-Router
Depositing User: Jisc Publications-Router
Date Deposited: 14 Oct 2019 08:49
Last Modified: 30 Oct 2019 05:55
URI: http://oro.open.ac.uk/id/eprint/67266
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