On superstatistical multiplicative-noise processes

TL;DR

This paper investigates the long-term behavior of non-stationary multiplicative-noise processes within the Feller class, extending superstatistics to include time-varying exponents and deriving a generalized Weibull distribution.

Contribution

It introduces a dynamical framework for superstatistical multiplicative processes with evolving exponents, generalizing previous static models and distributions.

Findings

Derived the long-term probability density function for non-stationary processes.

Established a dynamical scenario for the emergence of a generalized Weibull distribution.

Extended superstatistics to include time-varying exponents in multiplicative noise processes.

Abstract

In this manuscript we analyse the long-term probability density function of non-stationary dynamical processes which are enclosed inward the Feller class of processes with time varying exponents for multiplicative noise. The update in the value of the exponent occurs in the same conditions presented by Beck and Cohen for superstatistics. Moreover, we are able to provide a dynamical scenario for the emergence of a generalisation of the Weibull distribution previously introduced.