TY - JOUR
T1 - First passage times of Lévy flights coexisting with subdiffusion
AU - Koren, Tal
AU - Klafter, Joseph
AU - Magdziarz, Marcin
PY - 2007/9/26
Y1 - 2007/9/26
N2 - We investigate both analytically and numerically the first passage time (FPT) problem in one dimension for anomalous diffusion processes in which Lévy flights and subdiffusion coexist. We analyze the FPT for three subclasses of Lévy stable motions: (i) symmetric Lévy motions characterized by Lévy index μ, 0<μ<2, and skewness parameter β=0, (ii) one-sided Lévy motions with μ, 0<μ<1, and skewness β=1, and (iii) two-sided skewed Lévy motions, the extreme case, 1<μ<2, and skewness β=-1. In all three cases the waiting times between successive jumps are heavy tailed with index α. We show that in all three cases the FPT distributions are power laws. Our findings extend earlier studies on FPTs of Lévy flights by considering the interplay between long rests and the Lévy long jumps.
AB - We investigate both analytically and numerically the first passage time (FPT) problem in one dimension for anomalous diffusion processes in which Lévy flights and subdiffusion coexist. We analyze the FPT for three subclasses of Lévy stable motions: (i) symmetric Lévy motions characterized by Lévy index μ, 0<μ<2, and skewness parameter β=0, (ii) one-sided Lévy motions with μ, 0<μ<1, and skewness β=1, and (iii) two-sided skewed Lévy motions, the extreme case, 1<μ<2, and skewness β=-1. In all three cases the waiting times between successive jumps are heavy tailed with index α. We show that in all three cases the FPT distributions are power laws. Our findings extend earlier studies on FPTs of Lévy flights by considering the interplay between long rests and the Lévy long jumps.
UR - http://www.scopus.com/inward/record.url?scp=34848892126&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.76.031129
DO - 10.1103/PhysRevE.76.031129
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:34848892126
SN - 1539-3755
VL - 76
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
M1 - 031129
ER -