Anomalous diffusion and semimartingales

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. Copyright (C) EPLA, 2009