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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 7246865, 7 pages
Research Article

Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion

1School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
2School of Science, Central South University of Forest and Technology, Changsha, Hunan 410004, China

Correspondence should be addressed to Long Shi

Received 6 February 2017; Accepted 23 March 2017; Published 4 April 2017

Academic Editor: Giorgio Kaniadakis

Copyright © 2017 Long Shi and Aiguo Xiao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 -stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when , normal diffusion when , and superdiffusion when . 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.