Space-time fractional diffusion equations and asymptotic behaviors of a coupled continuous time random walk model

Long Shi, Zuguo Yu, Zhi Mao, Aiguo Xiao, Hailan Huang

Published 2013-08-12Version 1

In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are discussed. The corresponding fractional diffusion equations are derived from the given asymptotic behaviors. Corresponding to the asymptotic behaviors of the joint probability density function in the Fourier-Laplace space, the asymptotic behaviors of the waiting time probability density and the conditional probability density for jump length are also discussed.