# Socioeconomic Gauging of Brown and Levy Power Motions

## TL;DR

This paper uses socioeconomic inequality concepts to measure and interpret the 'degree of anomaly' in power Brownian and Levy motions, which are models of anomalous diffusion.

## Contribution

A novel socioeconomic-inequality-based framework is introduced to quantify anomalous behaviors in power motions.

## Key findings

- Socioeconomic indices provide quantitative scores for sub-diffusion, super-diffusion, and other anomalous behaviors.
- The approach interprets persistence and aging in power motions through inequality metrics.
- The method is generalizable to other anomalous-diffusion models.

## Abstract

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.