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

摘要

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