Generalized Master Equation for Space-Time Coupled Continuous Time Random Walk

Abstract

© 2017 Chinese Physical Society and IOP Publishing Ltd. The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function g(t) ~ t?, 0 = ? < 2, and the probability density function w(t) of a particle's waiting time t follows a power law form for large t: w(t) ~ t-(1+a), 0 < a < 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent ? and the long-tailed index a of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.