First passage times of Lévy flights coexisting with subdiffusion.
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 mu, 0<mu<2, and skewness parameter beta=0, (ii) one-sided Lévy motions with mu , 0<mu<1, and skewness beta=1, and (iii) two-sided skewed Lévy motions, the extreme case, 1<mu<2, and skewness beta=-1. In all three cases the waiting times between successive jumps are heavy tailed with index alpha. 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.
Koren
Tal
T
School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel. korenbta@post.tau.ac.il
Klafter
Joseph
J
Magdziarz
Marcin
M