Socioeconomic Gauging of Brown and Levy Power Motions

Recently introduced, power Brownian motion and power Levy motion are versatile and practical anomalous-diffusion models. On the one hand, the power motions are easily constructed and are easily tracked. On the other hand, the power motions display an assortment of anomalous behaviors including: sub-diffusion and super-diffusion; aging and anti-aging; and persistence and anti-persistence. This paper investigates the power motions from a socioeconomic-inequality perspective. Using this perspective, key statistical and temporal behaviors of the power motions are interpreted and scored. In particular, the paper provides simple and explicit quantitative answers-which are based on socioeconomic inequality indices-to the following question: what is the 'degree of anomaly' of each of the power-motions' anomalous behaviors? The socioeconomic approach presented in this paper may be applied (in future research) to additional anomalous-diffusion models.