Stochastic origin of Gompertzian growths

TL;DR

This paper explains the logarithmic nature of Gompertzian growth as emerging from a stochastic process, using a variational principle to model self-regulation and control of growth.

Contribution

It introduces a stochastic framework that derives Gompertzian growth from a log-normal process and incorporates feedback mechanisms for growth regulation.

Findings

Gompertz equation describes median evolution of a log-normal stochastic process.

A stochastic variational principle models self-regulating growth.

Framework enables external control of growth dynamics.

Abstract

This work faces the problem of the origin of the logarithmic character of the Gompertzian growth. We show that the macroscopic, deterministic Gompertz equation describes the evolution from the initial state to the final stationary value of the median of a log-normally distributed, stochastic process. Moreover, by exploiting a stochastic variational principle, we account for self-regulating feature of Gompertzian growths provided by self-consistent feedback of relative density variations. This well defined conceptual framework shows its usefulness by allowing a reliable control of the growth by external actions.