Modeling anomalous diffusion by a subordinated integrated Brownian motion
type: Item
instance of: scholarly article
title: Modeling anomalous diffusion by a subordinated integrated Brownian motion
zbMATH Open document ID: 1400.60102
DOI: 10.1155/2017/7246865
author: Yanyan Li
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: 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 \(\alpha\)-stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when \(0 < \alpha < 1 / 3\), normal diffusion when \(\alpha = 1 / 3\), and superdiffusion when \(1 / 3 < \alpha < 1\). 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.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 82C31
zbMATH DE Number: 6962664
zbMATH Keywords: integrated Brownian motion
zbMATH Keywords: subdiffusion
zbMATH Keywords: weak ergodicity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/7246865
OpenAlex ID: W2604275707
Wikidata QID: Q59142465
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description: scientific article; zbMATH DE number 6962664