TY - JOUR

T1 - On the first passage time and leapover properties of Lévy motions

AU - Koren, T.

AU - Chechkin, A. V.

AU - Klafter, J.

N1 - Funding Information:
The authors acknowledge discussions with Eli Barkai, Iddo Eliazar, Michael Andersen Lomholt and Ralf Metzler. AVC acknowledges hospitality of the School of Chemistry, Tel Aviv University. JK acknowledges the support of DFG Grant Ha 1517/26-1,2 (“Single molecules”).

PY - 2007/6/1

Y1 - 2007/6/1

N2 - We investigate two coupled properties of Lévy stable random motions: the first passage times (FPTs) and the first passage leapovers (FPLs). While, in general, the FPT problem has been studied quite extensively, the FPL problem has hardly attracted any attention. Considering a particle that starts at the origin and performs random jumps with independent increments chosen from a Lévy stable probability law λα,β(x), the FPT measures how long it takes the particle to arrive at or cross a target. The FPL addresses a different question: given that the first passage jump crosses the target, then how far does it get beyond the target? These two properties are investigated for three subclasses of Lévy stable motions: (i) symmetric Lévy motions characterized by Lévy index α(0<α<2) and skewness parameter β=0, (ii) one-sided Lévy motions with 0<α<1, β=1, and (iii) two-sided skewed Lévy motions, the extreme case, 1<α<2, β=-1.

AB - We investigate two coupled properties of Lévy stable random motions: the first passage times (FPTs) and the first passage leapovers (FPLs). While, in general, the FPT problem has been studied quite extensively, the FPL problem has hardly attracted any attention. Considering a particle that starts at the origin and performs random jumps with independent increments chosen from a Lévy stable probability law λα,β(x), the FPT measures how long it takes the particle to arrive at or cross a target. The FPL addresses a different question: given that the first passage jump crosses the target, then how far does it get beyond the target? These two properties are investigated for three subclasses of Lévy stable motions: (i) symmetric Lévy motions characterized by Lévy index α(0<α<2) and skewness parameter β=0, (ii) one-sided Lévy motions with 0<α<1, β=1, and (iii) two-sided skewed Lévy motions, the extreme case, 1<α<2, β=-1.

KW - Brownian motion

KW - First passage time

KW - Leapover

KW - Lévy motion

KW - Lévy stable distributions

UR - http://www.scopus.com/inward/record.url?scp=33947434422&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2006.12.039

DO - 10.1016/j.physa.2006.12.039

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AN - SCOPUS:33947434422

SN - 0378-4371

VL - 379

SP - 10

EP - 22

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

ER -