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

Long Shi

Advances in Mathematical Physics, 2019, vol. 2019, issue 1

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

Date: 2019
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https://doi.org/10.1155/2019/3479715

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:3479715

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