Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion
We consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse α-stable subordinator. We compute the mean square displace...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/7246865 |
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| _version_ | 1832568515171713024 |
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| author | Long Shi Aiguo Xiao |
| author_facet | Long Shi Aiguo Xiao |
| author_sort | Long Shi |
| collection | DOAJ |
| description | We consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse α-stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when 0<α<1/3, normal diffusion when α=1/3, and superdiffusion when 1/3<α<1. The time-averaged mean square displacement is also employed to show weak ergodicity breaking occurring in the proposed process. An extension to the fractional case is also considered. |
| format | Article |
| id | doaj-art-a10d3331dc4f49fe84855748afc4fb14 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-a10d3331dc4f49fe84855748afc4fb142025-02-03T00:58:53ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/72468657246865Modeling Anomalous Diffusion by a Subordinated Integrated Brownian MotionLong Shi0Aiguo Xiao1School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, ChinaSchool of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, ChinaWe consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse α-stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when 0<α<1/3, normal diffusion when α=1/3, and superdiffusion when 1/3<α<1. The time-averaged mean square displacement is also employed to show weak ergodicity breaking occurring in the proposed process. An extension to the fractional case is also considered.http://dx.doi.org/10.1155/2017/7246865 |
| spellingShingle | Long Shi Aiguo Xiao Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion Advances in Mathematical Physics |
| title | Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion |
| title_full | Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion |
| title_fullStr | Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion |
| title_full_unstemmed | Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion |
| title_short | Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion |
| title_sort | modeling anomalous diffusion by a subordinated integrated brownian motion |
| url | http://dx.doi.org/10.1155/2017/7246865 |
| work_keys_str_mv | AT longshi modelinganomalousdiffusionbyasubordinatedintegratedbrownianmotion AT aiguoxiao modelinganomalousdiffusionbyasubordinatedintegratedbrownianmotion |