TY - JOUR
A1 - Palyulin, Vladimir V
A1 - Blackburn, George
A1 - Lomholt, Michael A
A1 - Watkins, Nicholas W
A1 - Metzler, Ralf
A1 - Klages, Rainer
A1 - Chechkin, Aleksei V.
T1 - First passage and first hitting times of Lévy flights and Lévy walks
JF - New Journal of Physics
N2 - 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.
KW - Lévy flights
KW - Lévy walks
KW - first-passage time
KW - first-hitting time
Y1 - 2019
U6 - http://dx.doi.org/10.1088/1367-2630/ab41bb
SN - 1367-2630
VL - 21
PB - Dt. Physikalische Ges.
CY - Bad Honnef
ER -
TY - GEN
A1 - Palyulin, Vladimir V
A1 - Blackburn, George
A1 - Lomholt, Michael A
A1 - Watkins, Nicholas W
A1 - Metzler, Ralf
A1 - Klages, Rainer
A1 - Chechkin, Aleksei V.
T1 - First passage and first hitting times of Lévy flights and Lévy walks
T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 785
KW - Lévy flights
KW - Lévy walks
KW - first-passage time
KW - first-hitting time
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-439832
SN - 1866-8372
IS - 785
ER -