Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk

Abstract EN

In this work, a generalization of continuous time random walk is considered, where the waiting times among the subsequent jumps are power-law correlated with kernel function M(t)=tρ(ρ>-1).

In a continuum limit, the correlated continuous time random walk converges in distribution a subordinated process.

The mean square displacement of the proposed process is computed, which is of the form 〈x2(t)〉∝tH=t1/(1+ρ+1/α).

The anomy exponent H varies from α to α/(1+α) when -1<ρ<0 and from α/(1+α) to 0 when ρ>0.

The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases.