Statistical test for anomalous diffusion based on empirical anomaly measure for Gaussian processes

Abstract

Gaussian processes with anomalous diffusion behavior are considered. A new statistical test for the model identification that is based on the empirical anomaly measure (EAM) is introduced. This measure is considered as the distance between the anomalous and normal diffusion. In particular, the main properties of the EAM based on the quadratic form representation of Gaussian processes are investigated. The effectiveness of the test is evaluated for the fractional Brownian motion. Theoretical results and simulation studies are supported by the analysis of experimental data describing the sub-diffusive motion of microspheres in agarose hydrogels.