Generalised cascades

TL;DR

This paper explores how stable probability density functions are affected when standard multiplicative cascades are extended using Borges' q-product, linking to non-extensive statistical mechanics.

Contribution

It introduces a generalization of multiplicative cascades using the q-product, connecting cascade models to non-extensive statistical mechanics.

Findings

Stable density functions are modified under the q-product generalization.

The generalized cascades exhibit different statistical properties from standard models.

Potential applications in complex systems and turbulence modeling.

Abstract

In this manuscript we give thought to the aftermath on the stable probability density function when standard multiplicative cascades are generalised cascades based on the $q$-product of Borges that emerged in the context of non-extensive statistical mechanics.