Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen
OPUS4-43983 misc Palyulin, Vladimir V; Blackburn, George; Lomholt, Michael A; Watkins, Nicholas W; Metzler, Ralf; Klages, Rainer; Chechkin, Aleksei V. First passage and first hitting times of Lévy flights and Lévy 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. 2019 25 Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe 785 urn:nbn:de:kobv:517-opus4-439832 10.25932/publishup-43983 Institut für Physik und Astronomie
OPUS4-43982 Wissenschaftlicher Artikel Palyulin, Vladimir V; Blackburn, George; Lomholt, Michael A; Watkins, Nicholas W; Metzler, Ralf; Klages, Rainer; Chechkin, Aleksei V. First passage and first hitting times of Lévy flights and Lévy 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. Bad Honnef Dt. Physikalische Ges. 2019 24 New Journal of Physics 21 10.1088/1367-2630/ab41bb Institut für Physik und Astronomie