TY - JOUR

T1 - First passage and first hitting times of Lévy flights and Lévy walks

AU - Palyulin, Vladimir V.

AU - Blackburn, George

AU - Lomholt, Michael A.

AU - Watkins, Nicholas W.

AU - Metzler, Ralf

AU - Klages, Rainer

AU - Chechkin, Aleksei V.

PY - 2019/10/11

Y1 - 2019/10/11

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.

AB - 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 - first-hitting time

KW - first-passage time

KW - Lévy flights

KW - Lévy walks

UR - http://www.scopus.com/inward/record.url?scp=85073822265&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/ab41bb

DO - 10.1088/1367-2630/ab41bb

M3 - Article

AN - SCOPUS:85073822265

VL - 21

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

IS - 10

M1 - 103028

ER -