Anomalous diffusion and semimartingalesA. Weron and M. Magdziarz
Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology Wyspianskiego 27, 50-370 Wroclaw, Poland, EU
received 27 February 2009; accepted in final form 5 June 2009; published June 2009
published online 10 July 2009
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.
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