TY  - JOUR
A1  - Xu, Pengbo
A1  - Deng, Weihua
A1  - Sandev, Trifce
T1  - Levy walk with parameter dependent velocity
T2  - Journal of physics : A, Mathematical and theoretical
N2  - To analyze stochastic processes, one often uses integral transform (Fourier and Laplace) methods. However, for the time-space coupled cases, e.g. the Levy walk, sometimes the integral transform method may fail. Here we provide a Hermite polynomial expansion approach, being complementary to the integral transform method, to the Levy walk. Two approaches are compared for some already known results. We also consider the generalized Levy walk with parameter dependent velocity. Namely, we consider the Levy walk with velocity which depends on the walking length or on the duration of each step. Some interesting features of the generalized Levy walk are observed, including the special shapes of the probability density function, the first passage time distributions, and various diffusive behaviors of the mean squared displacement.
KW  - Hermite polynomial expansion
KW  - Levy walk
KW  - anomalous diffusion
KW  - parameter
KW  - dependent velocity
Y1  - 2020
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/60621
SN  - 1751-8113
SN  - 1751-8121
VL  - 53
IS  - 11
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -