Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion. (4th April 2017)

• Record Type: Journal Article
• Authors: Shi, Long; Xiao, Aiguo
• Other Names: Kaniadakis Giorgio Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2017(2017)
• Publication Date: 2017-04-04
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2017/7246865
• Languages: English
• ISSNs: 1687-9120

Abstract

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 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.