Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion

Long Shi and Aiguo Xiao

Advances in Mathematical Physics, 2017, vol. 2017, 1-7

Abstract:

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:7246865

DOI: 10.1155/2017/7246865

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