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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/3479715 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832568500309196800 |
|---|---|
| author | Long Shi |
| author_facet | Long Shi |
| author_sort | Long Shi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-645c1a1d8059459b9a1dc6372c0903db |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-645c1a1d8059459b9a1dc6372c0903db2025-02-03T00:58:56ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/34797153479715Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random WalkLong Shi0School of Science, Hunan Institute of Engineering, Xiangtan, Hunan 411104, ChinaIn 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.http://dx.doi.org/10.1155/2019/3479715 |
| spellingShingle | Long Shi Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk Advances in Mathematical Physics |
| title | Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk |
| title_full | Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk |
| title_fullStr | Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk |
| title_full_unstemmed | Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk |
| title_short | Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk |
| title_sort | generalized diffusion equation associated with a power law correlated continuous time random walk |
| url | http://dx.doi.org/10.1155/2019/3479715 |
| work_keys_str_mv | AT longshi generalizeddiffusionequationassociatedwithapowerlawcorrelatedcontinuoustimerandomwalk |