Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk
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 pr...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/3479715 |
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| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |