Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk. (2nd June 2019) - Shi, Long
Abstract : 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 functionM ( t ) = t ρ ( 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〈 x 2 ( t ) 〉 ∝ t H = t 1 / ( 1 + ρ + 1 / α ) . The anomy exponentH varies fromα toα / ( 1 + α ) when- 1 < ρ < 0 and fromα / ( 1 + α ) to0 whenρ > 0 . The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases.