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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |