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

dc.contributor.authorPalyulin, Vladimir V.
dc.contributor.authorBlackburn, George
dc.contributor.authorLomholt, Michael A.
dc.contributor.authorWatkins, Nicholas W.
dc.contributor.authorMetzler, Ralf
dc.contributor.authorKlages, Rainer
dc.contributor.authorChechkin, Aleksei V.
dc.date.accessioned2022-02-17T15:05:21Z
dc.date.available2022-02-17T15:05:21Z
dc.date.issued2019-10-11
dc.date.updated2022-02-11T12:45:56Z
dc.description.abstractFor 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.en
dc.identifier.eissn1367-2630
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/16436
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-15212
dc.language.isoenen
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/en
dc.subject.ddc530 Physikde
dc.subject.otherLévy flightsen
dc.subject.otherLévy walksen
dc.subject.otherfirst-passage timeen
dc.subject.otherfirst-hitting timeen
dc.titleFirst passage and first hitting times of Lévy flights and Lévy walksen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.articlenumber103028en
dcterms.bibliographicCitation.doi10.1088/1367-2630/ab41bben
dcterms.bibliographicCitation.issue10en
dcterms.bibliographicCitation.journaltitleNew Journal of Physicsen
dcterms.bibliographicCitation.originalpublishernameIOPen
dcterms.bibliographicCitation.originalpublisherplaceBristolen
dcterms.bibliographicCitation.volume21en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Theoretische Physik>FG Nichtlineare Dynamik und Kontrollede
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupFG Nichtlineare Dynamik und Kontrollede
tub.affiliation.instituteInst. Theoretische Physikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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