Issue
EPL
Volume 86, Number 6, June 2009
Article Number 60010
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/86/60010
Published online 10 July 2009
EPL, 86 (2009) 60010
DOI: 10.1209/0295-5075/86/60010

Anomalous diffusion and semimartingales

A. Weron and M. Magdziarz

Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology Wyspianskiego 27, 50-370 Wroclaw, Poland, EU

marcin.magdziarz@pwr.wroc.pl

received 27 February 2009; accepted in final form 5 June 2009; published June 2009
published online 10 July 2009

Abstract
We argue that the essential part of the currently explored models of anomalous (non-Brownian) diffusion are actually Brownian motion subordinated by the appropriate random time. Thus, in many cases, anomalous diffusion can be embedded in Brownian diffusion. Such an embedding takes place if and only if the anomalous diffusion is a semimartingale process. We also discuss the structure of anomalous diffusion models. Categorization of semimartingales can be applied to differentiate among various anomalous processes. In particular, identification of the type of subdiffusive dynamics from experimental data is feasible.

PACS
05.40.Fb - Random walks and Levy flights.
02.50.Ey - Stochastic processes.
05.10.-a - Computational methods in statistical physics and nonlinear dynamics.

© EPLA 2009