Comment on 'Anomalous diffusion induced by enhancement of memory'

TL;DR

This paper comments on previous models of anomalous diffusion with memory, showing they are mathematically equivalent and can be mapped onto each other, clarifying their relationship.

Contribution

It demonstrates the equivalence of two memory-dependent random walk models, unifying their mathematical framework and expectation values.

Findings

Models are mathematically equivalent

Expectation values are identical under parameter mapping

Clarifies the relationship between two prior models

Abstract

In a recent paper [2] the author introduced and investigated a random walk model similar to a model introduced in [1]. In these models the increment of the random walk depends on the complete past of the process. In this note I will point out that the models considered in [1] and [2] can be mapped onto each other one to one. They can be defined on a common probability space and hence all expectation values of the model [2] with parameter p are equal to the ones of [1] with a corresponding parameter $\tilde{p}$.